# Glossary

- Page ID
- 51361

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Words (or words that have the same definition) | The definition is case sensitive | (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages] | (Optional) Caption for Image | (Optional) External or Internal Link | (Optional) Source for Definition |
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(Eg. "Genetic, Hereditary, DNA ...") | (Eg. "Relating to genes or heredity") | The infamous double helix | https://bio.libretexts.org/ | CC-BY-SA; Delmar Larsen |

Word(s) | Definition | Image | Caption | Link | Source |
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Applications involving simple interest and money. | |||||

Applications involving a mixture of amounts usually given as a percentage of some total. | |||||

Applications relating distance, average rate, and time. | |||||

absolute value | The distance from the graph of a number a to zero on a number line, denoted $\left|a\right|.$ |
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absolute value function | The function defined by $f(x)=\left|x\right|.$ | ||||

AC method | Method used for factoring trinomials by replacing the middle term with two terms that allow us to factor the resulting four-term polynomial by grouping. | ||||

addition property of equations | If A, B, C, and D are algebraic expressions, where A = B and C = D, then A + C = B + D. |
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addition property of equations | If A, B, C, and D are algebraic expressions, where A = B and C = D, then A + C = B + D. |
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algebraic expressions | Combinations of variables and numbers along with mathematical operations used to generalize specific arithmetic operations. | ||||

argument of the absolute value | The number or expression inside the absolute value. | ||||

argument of the absolute value | The number or expression inside the absolute value. | ||||

argument of the function | The value or algebraic expression used as input when using function notation. | ||||

arithmetic means | The terms between given terms of an arithmetic sequence. | ||||

arithmetic progression | Used when referring to an arithmetic sequence. | ||||

arithmetic series | The sum of the terms of an arithmetic sequence. | ||||

arithmetic series | The sum of the terms of an arithmetic sequence. | ||||

augmented matrix | The coefficient matrix with the column of constants included. | ||||

augmented matrix | The coefficient matrix with the column of constants included. | ||||

average cost | The total cost divided by the number of units produced, which can be represented by $\stackrel{\u2013}{C}(x)=\frac{C(x)}{x}$, where $C(x)$ is a cost function. | ||||

average cost | The total cost divided by the number of units produced, which can be represented by $\stackrel{\u2013}{C}(x)=\frac{C(x)}{x}$, where $C(x)$ is a cost function. | ||||

axis of symmetry | A term used when referencing the line of symmetry. | ||||

axis of symmetry | A term used when referencing the line of symmetry. | ||||

Back substitute | Once a value is found for a variable, substitute it back into one of the original equations, or its equivalent, to determine the corresponding value of the other variable. | ||||

Back substitute | Once a value is found for a variable, substitute it back into one of the original equations, or its equivalent, to determine the corresponding value of the other variable. | ||||

binomial | Polynomial with two terms. | ||||

binomial coefficient | An integer that is calculated using the formula: $\left(\begin{array}{c}n\\ k\end{array}\right)=\frac{n!}{k!\left(n-k\right)!}.$ | ||||

binomial coefficient | An integer that is calculated using the formula: $\left(\begin{array}{c}n\\ k\end{array}\right)=\frac{n!}{k!\left(n-k\right)!}.$ | ||||

binomial theorem | Describes the algebraic expansion of binomials raised to powers: $\begin{array}{c}{\left(x+y\right)}^{n}\hfill \\ =\text{\hspace{0.17em}}{\displaystyle \underset{k=0}{\overset{n}{\Sigma}}\text{\hspace{0.17em}}\left(\begin{array}{c}n\\ k\end{array}\right)}\text{\hspace{0.17em}}{x}^{n-k}{y}^{k}.\end{array}$ | ||||

binomial theorem | Describes the algebraic expansion of binomials raised to powers: $\begin{array}{c}{\left(x+y\right)}^{n}\hfill \\ =\text{\hspace{0.17em}}{\displaystyle \underset{k=0}{\overset{n}{\Sigma}}\text{\hspace{0.17em}}\left(\begin{array}{c}n\\ k\end{array}\right)}\text{\hspace{0.17em}}{x}^{n-k}{y}^{k}.\end{array}$ | ||||

breakeven point | The point at which profit is neither negative nor positive; profit is equal to zero. | ||||

breakeven point | The point at which profit is neither negative nor positive; profit is equal to zero. | ||||

Cartesian coordinate system | Term used in honor of René Descartes when referring to the rectangular coordinate system. | ||||

Cartesian coordinate system | Term used in honor of René Descartes when referring to the rectangular coordinate system. | ||||

change of base formula | ${}_{}$a logarithm in terms of base-b logarithms using this formula. |
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change of base formula | ${}_{}$a logarithm in terms of base-b logarithms using this formula. |
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circle in general form | The equation of a circle written in the form ${x}^{2}+{y}^{2}+cx+dy+e=0.$ | ||||

circle in general form | The equation of a circle written in the form ${x}^{2}+{y}^{2}+cx+dy+e=0.$ | ||||

circle in standard form | The equation of a circle written in the form ${\left(x-h\right)}^{2}+{\left(y-k\right)}^{2}={r}^{2}$ where $\left(h,k\right)$ is the center and r is the radius. |
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circle in standard form | The equation of a circle written in the form ${\left(x-h\right)}^{2}+{\left(y-k\right)}^{2}={r}^{2}$ where $\left(h,k\right)$ is the center and r is the radius. |
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co-vertices | Points on the ellipse that mark the endpoints of the minor axis. | ||||

co-vertices | Points on the ellipse that mark the endpoints of the minor axis. | ||||

codomain | Used when referencing the range. | ||||

codomain | Used when referencing the range. | ||||

coefficient matrix | The matrix of coefficients of a linear system in standard form written as they appear lined up without the variables or operations. | ||||

coefficient matrix | The matrix of coefficients of a linear system in standard form written as they appear lined up without the variables or operations. | ||||

combining like terms | Adding or subtracting like terms within an algebraic expression to obtain a single term with the same variable part. | ||||

combining like terms | Adding or subtracting like terms within an algebraic expression to obtain a single term with the same variable part. | ||||

common denominator | A denominator that is shared by more than one fraction. | ||||

common denominator | A denominator that is shared by more than one fraction. | ||||

common difference | The constant d that is obtained from subtracting any two successive terms of an arithmetic sequence; ${a}_{n}-{a}_{n-1}=d.$ |
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common difference | The constant d that is obtained from subtracting any two successive terms of an arithmetic sequence; ${a}_{n}-{a}_{n-1}=d.$ |
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common factor | A factor that is shared by more than one real number. | ||||

common factor | A factor that is shared by more than one real number. | ||||

common logarithm | The logarithm base 10, denoted $\mathrm{log}\text{\hspace{0.17em}}x.$ | ||||

common logarithm | The logarithm base 10, denoted $\mathrm{log}\text{\hspace{0.17em}}x.$ | ||||

common ratio | The constant r that is obtained from dividing any two successive terms of a geometric sequence; $\frac{{a}_{n}}{{a}_{n-1}}=r.$ |
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common ratio | The constant r that is obtained from dividing any two successive terms of a geometric sequence; $\frac{{a}_{n}}{{a}_{n-1}}=r.$ |
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completely factored | A polynomial that is prime or written as a product of prime polynomials. | ||||

completely factored | A polynomial that is prime or written as a product of prime polynomials. | ||||

completing the square | The process of rewriting a quadratic equation to be in the form ${\left(x-p\right)}^{2}=q.$ | ||||

completing the square | The process of rewriting a quadratic equation to be in the form ${\left(x-p\right)}^{2}=q.$ | ||||

complex conjugate | Two complex numbers whose real parts are the same and imaginary parts are opposite. If given $a+bi$, then its complex conjugate is $a-bi.$ | ||||

complex conjugate | Two complex numbers whose real parts are the same and imaginary parts are opposite. If given $a+bi$, then its complex conjugate is $a-bi.$ | ||||

complex rational expression | A rational expression that contains one or more rational expressions in the numerator or denominator or both. | ||||

complex rational expression | A rational expression that contains one or more rational expressions in the numerator or denominator or both. | ||||

composition operator | The open dot used to indicate the function composition $\left(f\u25cbg\right)\left(x\right)=f\left(g\left(x\right)\right).$ | ||||

composition operator | The open dot used to indicate the function composition $\left(f\u25cbg\right)\left(x\right)=f\left(g\left(x\right)\right).$ | ||||

compound inequalities | Two or more inequalities in one statement joined by the word “and” or by the word “or.” | ||||

compound inequalities | Two or more inequalities in one statement joined by the word “and” or by the word “or.” | ||||

compound interest formula | A formula that gives the amount accumulated by earning interest on principal and interest over time: $A\left(t\right)=P{\left(1+\frac{r}{n}\right)}^{nt}.$ | ||||

compound interest formula | A formula that gives the amount accumulated by earning interest on principal and interest over time: $A\left(t\right)=P{\left(1+\frac{r}{n}\right)}^{nt}.$ | ||||

conic section | A curve obtained from the intersection of a right circular cone and a plane. | ||||

conic section | A curve obtained from the intersection of a right circular cone and a plane. | ||||

conjugate axis | A line segment through the center of a hyperbola that is perpendicular to the transverse axis. | ||||

conjugate axis | A line segment through the center of a hyperbola that is perpendicular to the transverse axis. | ||||

conjugate binomials | The binomials $\left(a+b\right)$ and $\left(a-b\right).$ | ||||

conjugate binomials | The binomials $\left(a+b\right)$ and $\left(a-b\right).$ | ||||

conjugates | The factors $\left(a+b\right)$ and $\left(a-b\right)$ are conjugates. | ||||

conjugates | The factors $\left(a+b\right)$ and $\left(a-b\right)$ are conjugates. | ||||

constant function | Any function of the form $f(x)=c$ where c is a real number. |
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constant function | Any function of the form $f(x)=c$ where c is a real number. |
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constant of proportionality | Used when referring to the constant of variation. | ||||

constant of proportionality | Used when referring to the constant of variation. | ||||

constant of variation | The nonzero multiple k, when quantities vary directly or inversely. |
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constant of variation | The nonzero multiple k, when quantities vary directly or inversely. |
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constant polynomial | A polynomial with degree 0. | ||||

constant term | A term written without a variable factor. | ||||

constant term | A term written without a variable factor. | ||||

continuously compounding interest formula | A formula that gives the amount accumulated by earning continuously compounded interest: $A\left(t\right)=P{e}^{rt}.$ | ||||

continuously compounding interest formula | A formula that gives the amount accumulated by earning continuously compounded interest: $A\left(t\right)=P{e}^{rt}.$ | ||||

contradiction | An equation that is never true and has no solution. | ||||

contradiction | An equation that is never true and has no solution. | ||||

convergent geometric series | An infinite geometric series where $\left|r\right|<1$ whose sum is given by the formula: ${S}_{\infty}=\frac{{a}_{1}}{1-r}.$ | ||||

convergent geometric series | An infinite geometric series where $\left|r\right|<1$ whose sum is given by the formula: ${S}_{\infty}=\frac{{a}_{1}}{1-r}.$ | ||||

cost function | A function that models the cost of producing a number of units. | ||||

cost function | A function that models the cost of producing a number of units. | ||||

Cramer’s rule | The solution to an independent system of linear equations expressed in terms of determinants. | ||||

Cramer’s rule | The solution to an independent system of linear equations expressed in terms of determinants. | ||||

critical numbers | The values in the domain of a function that separate regions that produce positive or negative results. | ||||

critical numbers | The values in the domain of a function that separate regions that produce positive or negative results. | ||||

cross multiplication | If $\text{\hspace{0.17em}}\frac{a}{b}=\frac{c}{d}$ then $ad=bc.$ | ||||

cross multiplication | If $\text{\hspace{0.17em}}\frac{a}{b}=\frac{c}{d}$ then $ad=bc.$ | ||||

cube | The result when the exponent of any real number is 3. | ||||

cube | The result when the exponent of any real number is 3. | ||||

cube root function | The function defined by $f\left(x\right)=\sqrt[3]{x}.$ | ||||

cube root function | The function defined by $f\left(x\right)=\sqrt[3]{x}.$ | ||||

cubing function | The cubic function defined by $f(x)={x}^{3}.$ | ||||

cubing function | The cubic function defined by $f(x)={x}^{3}.$ | ||||

degree of a polynomial | The largest degree of all of its terms. | ||||

degree of a polynomial | The largest degree of all of its terms. | ||||

degree of a term | The exponent of the variable. If there is more than one variable in the term, the degree of the term is the sum their exponents. | ||||

degree of a term | The exponent of the variable. If there is more than one variable in the term, the degree of the term is the sum their exponents. | ||||

dependent system | A linear system with two variables that consists of equivalent equations. It has infinitely many ordered pair solutions, denoted by $\left(x,mx+b\right)$. | ||||

dependent system | A linear system with two variables that consists of equivalent equations. It has infinitely many ordered pair solutions, denoted by $\left(x,mx+b\right)$. | ||||

dependent variable | The variable whose value is determined by the value of the independent variable. Usually we think of the y-value of an ordered pair (x, y) as the dependent variable. |
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dependent variable | The variable whose value is determined by the value of the independent variable. Usually we think of the y-value of an ordered pair (x, y) as the dependent variable. |
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determinant | A real number associated with a square matrix. | ||||

determinant | A real number associated with a square matrix. | ||||

diameter | The length of a line segment passing through the center of a circle whose endpoints are on the circle. | ||||

diameter | The length of a line segment passing through the center of a circle whose endpoints are on the circle. | ||||

difference | The result of subtracting. | ||||

difference | The result of subtracting. | ||||

difference of cubes | $\begin{array}{l}{a}^{3}-{b}^{3}\hfill \\ =(a-b)({a}^{2}+ab+{b}^{2})\hfill \end{array}$, where a and b represent algebraic expressions. |
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difference of cubes | $\begin{array}{l}{a}^{3}-{b}^{3}\hfill \\ =(a-b)({a}^{2}+ab+{b}^{2})\hfill \end{array}$, where a and b represent algebraic expressions. |
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difference of squares | The special product obtained by multiplying conjugate binomials $\left(a+b\right)\left(a-b\right)={a}^{2}-{b}^{2}.$ | ||||

difference of squares | The special product obtained by multiplying conjugate binomials $\left(a+b\right)\left(a-b\right)={a}^{2}-{b}^{2}.$ | ||||

difference of squares | ${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right),$ where a and b represent algebraic expressions. |
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difference of squares | ${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right),$ where a and b represent algebraic expressions. |
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difference quotient | The mathematical quantity $\frac{f\left(x+h\right)-f\left(x\right)}{h}$, where $h\ne 0$, which represents the slope of a secant line through a function f. |
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difference quotient | The mathematical quantity $\frac{f\left(x+h\right)-f\left(x\right)}{h}$, where $h\ne 0$, which represents the slope of a secant line through a function f. |
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dilation | A non-rigid transformation, produced by multiplying functions by a nonzero real number, which appears to stretch the graph either vertically or horizontally. | ||||

dilation | A non-rigid transformation, produced by multiplying functions by a nonzero real number, which appears to stretch the graph either vertically or horizontally. | ||||

discriminant | The expression inside the radical of the quadratic formula, ${b}^{2}-4ac.$ | ||||

discriminant | The expression inside the radical of the quadratic formula, ${b}^{2}-4ac.$ | ||||

distance formula | Given two points $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ and $({x}_{2},\text{\hspace{0.17em}}{y}_{2})$, calculate the distance d between them using the formula $\begin{array}{l}d=\hfill \\ \sqrt{{({x}_{2}-{x}_{1})}^{2}+{({y}_{2}-{y}_{1})}^{2}}.\hfill \end{array}$ |
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distance formula | Given two points $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ and $({x}_{2},\text{\hspace{0.17em}}{y}_{2})$, calculate the distance d between them using the formula $\begin{array}{l}d=\hfill \\ \sqrt{{({x}_{2}-{x}_{1})}^{2}+{({y}_{2}-{y}_{1})}^{2}}.\hfill \end{array}$ |
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distance formula | Given two points $\left({x}_{1},\hspace{0.17em}{y}_{1}\right)$ and $\left({x}_{2},\hspace{0.17em}{y}_{2}\right)$, the distance d between them is given by $\begin{array}{c}d=\hfill \\ \sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}\hfill \end{array}$. |
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distance formula | Given two points $\left({x}_{1},\hspace{0.17em}{y}_{1}\right)$ and $\left({x}_{2},\hspace{0.17em}{y}_{2}\right)$, the distance d between them is given by $\begin{array}{c}d=\hfill \\ \sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}\hfill \end{array}$. |
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distributive property | Given any real numbers a, b, and c, $a\left(b+c\right)=ab+ac$ or $\left(b+c\right)a=ba+ca.$ |
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distributive property | Given any real numbers a, b, and c, $a\left(b+c\right)=ab+ac$ or $\left(b+c\right)a=ba+ca.$ |
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division | Divide functions as indicated by the notation: $\left(f/g\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$, where $g\left(x\right)\ne 0.$ | ||||

division | Divide functions as indicated by the notation: $\left(f/g\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$, where $g\left(x\right)\ne 0.$ | ||||

double root | A root that is repeated twice. | ||||

double root | A root that is repeated twice. | ||||

double-negative property | The opposite of a negative number is positive: −(−a) = a. |
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double-negative property | The opposite of a negative number is positive: −(−a) = a. |
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doubling time | The period of time it takes a quantity to double. | ||||

doubling time | The period of time it takes a quantity to double. | ||||

element | An object within a set. | ||||

element | An object within a set. | ||||

elementary row operations | Operations that can be performed to obtain equivalent linear systems. | ||||

elementary row operations | Operations that can be performed to obtain equivalent linear systems. | ||||

ellipse | The set of points in a plane whose distances from two fixed points have a sum that is equal to a positive constant. | ||||

ellipse | The set of points in a plane whose distances from two fixed points have a sum that is equal to a positive constant. | ||||

ellipse in general form | The equation of an ellipse written in the form $$ |
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ellipse in general form | The equation of an ellipse written in the form $$ |
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ellipse in standard form | The equation of an ellipse written in the form $\frac{{\left(x-h\right)}^{}}{}$a and b is the major radius and the smaller is the minor radius. |
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ellipse in standard form | The equation of an ellipse written in the form $\frac{{\left(x-h\right)}^{}}{}$a and b is the major radius and the smaller is the minor radius. |
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empty set | A subset with no elements, denoted Ø or { }. | ||||

empty set | A subset with no elements, denoted Ø or { }. | ||||

equivalent equations | Equations with the same solution set. | ||||

equivalent equations | Equations with the same solution set. | ||||

equivalent fractions | Two equal fractions expressed using different numerators and denominators. | ||||

equivalent fractions | Two equal fractions expressed using different numerators and denominators. | ||||

equivalent inequality | Inequalities that share the same solution set. | ||||

equivalent inequality | Inequalities that share the same solution set. | ||||

equivalent system | A system consisting of equivalent equations that share the same solution set. | ||||

equivalent system | A system consisting of equivalent equations that share the same solution set. | ||||

evaluating | The process of performing the operations of an algebraic expression for given values of the variables. | ||||

evaluating | The process of performing the operations of an algebraic expression for given values of the variables. | ||||

even integers | Integers that are divisible by 2. | ||||

even integers | Integers that are divisible by 2. | ||||

exponent | The positive integer n in the exponential notation ${a}^{n}$ that indicates the number of times the base is used as a factor. |
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exponent | The positive integer n in the exponential notation ${a}^{n}$ that indicates the number of times the base is used as a factor. |
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exponential form | An equivalent expression written using a rational exponent. | ||||

exponential form | An equivalent expression written using a rational exponent. | ||||

exponential function | Any function with a definition of the form $f\left(x\right)={b}^{x}$ where $b>0$ and $b\ne 1.$ | ||||

exponential function | Any function with a definition of the form $f\left(x\right)={b}^{x}$ where $b>0$ and $b\ne 1.$ | ||||

exponential growth/decay formula | A formula that models exponential growth or decay: $P\left(t\right)=$ |
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exponential growth/decay formula | A formula that models exponential growth or decay: $P\left(t\right)=$ |
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exponential notation | The compact notation ${a}^{n}$ used when a factor a is repeated n times. |
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exponential notation | The compact notation ${a}^{n}$ used when a factor a is repeated n times. |
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extracting the root | Applying the square root property as a means of solving a quadratic equation. | ||||

extracting the root | Applying the square root property as a means of solving a quadratic equation. | ||||

extraneous solutions | A solution that does not solve the original equation. | ||||

extraneous solutions | A solution that does not solve the original equation. | ||||

extraneous solutions | A properly found solution that does not solve the original equation. | ||||

extraneous solutions | A properly found solution that does not solve the original equation. | ||||

extrapolation | Using a linear function to estimate values that extend beyond the given data points. | ||||

extrapolation | Using a linear function to estimate values that extend beyond the given data points. | ||||

factorial | The product of all natural numbers less than or equal to a given natural number, denoted n!. |
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factorial | The product of all natural numbers less than or equal to a given natural number, denoted n!. |
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Factoring by grouping | A technique for factoring polynomials with four terms. | ||||

Factoring by grouping | A technique for factoring polynomials with four terms. | ||||

Factoring out the greatest common factor (GCF) | The process of rewriting a polynomial as a product using the GCF of all of its terms. | ||||

Factoring out the greatest common factor (GCF) | The process of rewriting a polynomial as a product using the GCF of all of its terms. | ||||

factors | Any of the numbers that form a product. | ||||

factors | Any of the numbers that form a product. | ||||

factors | Any of the numbers or expressions that form a product. | ||||

factors | Any of the numbers or expressions that form a product. | ||||

finite sequence | A sequence whose domain is $\left\{1,2,3,\mathrm{\dots},k\right\}$ where k is a natural number. |
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finite sequence | A sequence whose domain is $\left\{1,2,3,\mathrm{\dots},k\right\}$ where k is a natural number. |
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floor function | A term used when referring to the greatest integer function. | ||||

floor function | A term used when referring to the greatest integer function. | ||||

formulas | A reusable mathematical model using algebraic expressions to describe a common application. | ||||

formulas | A reusable mathematical model using algebraic expressions to describe a common application. | ||||

fraction | A rational number written as a quotient of two integers: $\frac{a}{b}$, where $b\ne 0.$ | ||||

fraction | A rational number written as a quotient of two integers: $\frac{a}{b}$, where $b\ne 0.$ | ||||

function | A relation where each element in the domain corresponds to exactly one element in the range. | ||||

function | A relation where each element in the domain corresponds to exactly one element in the range. | ||||

function notation | The notation $f\left(x\right)=y$, which reads “f of x is equal to y.” Given a function, y and $f\left(x\right)$ can be used interchangeably. |
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function notation | The notation $f\left(x\right)=y$, which reads “f of x is equal to y.” Given a function, y and $f\left(x\right)$ can be used interchangeably. |
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fundamental rectangle | The rectangle formed using the endpoints of a hyperbolas, transverse and conjugate axes. | ||||

fundamental rectangle | The rectangle formed using the endpoints of a hyperbolas, transverse and conjugate axes. | ||||

fundamental theorem of algebra | Guarantees that there will be as many (or fewer) roots to a polynomial function with one variable as its degree. | ||||

fundamental theorem of algebra | Guarantees that there will be as many (or fewer) roots to a polynomial function with one variable as its degree. | ||||

fundamental theorem of algebra | If multiple roots and complex roots are counted, then every polynomial with one variable will have as many roots as its degree. | ||||

fundamental theorem of algebra | If multiple roots and complex roots are counted, then every polynomial with one variable will have as many roots as its degree. | ||||

Gaussian elimination | Steps used to obtain an equivalent linear system in upper triangular form so that it can be solved using back substitution. | ||||

Gaussian elimination | Steps used to obtain an equivalent linear system in upper triangular form so that it can be solved using back substitution. | ||||

general term of a sequence | An equation that defines the nth term of a sequence commonly denoted using subscripts ${a}_{n}.$ |
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general term of a sequence | An equation that defines the nth term of a sequence commonly denoted using subscripts ${a}_{n}.$ |
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geometric means | The terms between given terms of a geometric sequence. | ||||

geometric means | The terms between given terms of a geometric sequence. | ||||

geometric progression | Used when referring to a geometric sequence. | ||||

geometric progression | Used when referring to a geometric sequence. | ||||

geometric series | The sum of the terms of a geometric sequence. | ||||

geometric series | The sum of the terms of a geometric sequence. | ||||

graph | A visual representation of a relation on a rectangular coordinate plane. | ||||

graph | A visual representation of a relation on a rectangular coordinate plane. | ||||

graph of the solution set | Solutions to an algebraic expression expressed on a number line. | ||||

graph of the solution set | Solutions to an algebraic expression expressed on a number line. | ||||

graphing method | A means of solving a system by graphing the equations on the same set of axes and determining where they intersect. | ||||

graphing method | A means of solving a system by graphing the equations on the same set of axes and determining where they intersect. | ||||

greatest common factor (GCF). | The largest shared factor of any number of integers. | ||||

greatest common factor (GCF). | The largest shared factor of any number of integers. | ||||

greatest common monomial factor (GCF) | The product of the common variable factors and the GCF of the coefficients. | ||||

greatest common monomial factor (GCF) | The product of the common variable factors and the GCF of the coefficients. | ||||

greatest integer function | The function that assigns any real number x to the greatest integer less than or equal to x denoted $f(x)=[[x]]$. |
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greatest integer function | The function that assigns any real number x to the greatest integer less than or equal to x denoted $f(x)=[[x]]$. |
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grouping symbols | Parentheses, brackets, braces, and the fraction bar are the common symbols used to group expressions and mathematical operations within a computation. | ||||

grouping symbols | Parentheses, brackets, braces, and the fraction bar are the common symbols used to group expressions and mathematical operations within a computation. | ||||

half-life | The period of time it takes a quantity to decay to one-half of the initial amount. | ||||

half-life | The period of time it takes a quantity to decay to one-half of the initial amount. | ||||

horizontal asymptote | A horizontal line to which a graph becomes infinitely close where the x-values tend toward ±∞. |
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horizontal asymptote | A horizontal line to which a graph becomes infinitely close where the x-values tend toward ±∞. |
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horizontal line test | If a horizontal line intersects the graph of a function more than once, then it is not one-to-one. | ||||

horizontal line test | If a horizontal line intersects the graph of a function more than once, then it is not one-to-one. | ||||

horizontal translation | A rigid transformation that shifts a graph left or right. | ||||

horizontal translation | A rigid transformation that shifts a graph left or right. | ||||

hyperbola | The set of points in a plane whose distances from two fixed points, called foci, has an absolute difference that is equal to a positive constant. | ||||

hyperbola | The set of points in a plane whose distances from two fixed points, called foci, has an absolute difference that is equal to a positive constant. | ||||

hyperbola in general form | The equation of a hyperbola written in the form $\begin{array}{ll}p{x}^{2}-q{y}^{2}+cx\hfill & \hfill \\ \hfill +dy+e& =\hfill & 0\hfill \end{array}$ or $\begin{array}{ll}q{y}^{2}-p{x}^{2}-cx\hfill & \hfill \\ \hfill +dy+e& =\hfill & 0\hfill \end{array}$ where $p,q>0.$ | ||||

hyperbola in general form | The equation of a hyperbola written in the form $\begin{array}{ll}p{x}^{2}-q{y}^{2}+cx\hfill & \hfill \\ \hfill +dy+e& =\hfill & 0\hfill \end{array}$ or $\begin{array}{ll}q{y}^{2}-p{x}^{2}-cx\hfill & \hfill \\ \hfill +dy+e& =\hfill & 0\hfill \end{array}$ where $p,q>0.$ | ||||

hyperbola opening left and right in standard form | The equation of a hyperbola written in the form $\frac{{\left(x-h\right)}^{2}}{{a}^{2}}-\frac{{\left(y-k\right)}^{}}{}$a defines the transverse axis, and b defines the conjugate axis. |
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hyperbola opening left and right in standard form | The equation of a hyperbola written in the form $\frac{{\left(x-h\right)}^{2}}{{a}^{2}}-\frac{{\left(y-k\right)}^{}}{}$a defines the transverse axis, and b defines the conjugate axis. |
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hyperbola opening upward and downward in standard form | The equation of a hyperbola written in the form $\frac{{\left(y-k\right)}^{2}}{{b}^{2}}-\frac{{\left(x-h\right)}^{}}{}$b defines the transverse axis, and a defines the conjugate axis. |
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hyperbola opening upward and downward in standard form | The equation of a hyperbola written in the form $\frac{{\left(y-k\right)}^{2}}{{b}^{2}}-\frac{{\left(x-h\right)}^{}}{}$b defines the transverse axis, and a defines the conjugate axis. |
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identity function | The linear function defined by $f(x)=x.$ | ||||

identity function | The linear function defined by $f(x)=x.$ | ||||

imaginary number | A square root of any negative real number. | ||||

imaginary number | A square root of any negative real number. | ||||

imaginary part | The real number b of a complex number $a+bi.$ |
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imaginary part | The real number b of a complex number $a+bi.$ |
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imaginary unit | Defined as $i=\sqrt{\text{\u2212}1}$ where ${i}^{2}=\text{\u2212}1.$ | ||||

imaginary unit | Defined as $i=\sqrt{\text{\u2212}1}$ where ${i}^{2}=\text{\u2212}1.$ | ||||

inclusive inequalities | Use the symbol $\le $ to express quantities that are “less than or equal to” and $\ge $ for quantities that are “greater than or equal to” each other. | ||||

inclusive inequalities | Use the symbol $\le $ to express quantities that are “less than or equal to” and $\ge $ for quantities that are “greater than or equal to” each other. | ||||

inconsistent system | A system with no simultaneous solution. | ||||

inconsistent system | A system with no simultaneous solution. | ||||

independent system | A linear system with two variables that has exactly one ordered pair solution. | ||||

independent system | A linear system with two variables that has exactly one ordered pair solution. | ||||

indeterminate | A quotient such as $\frac{0}{0}$ is a quantity that is uncertain or ambiguous. | ||||

indeterminate | A quotient such as $\frac{0}{0}$ is a quantity that is uncertain or ambiguous. | ||||

index | The positive integer n in the notation $\sqrt[n]{\text{\hspace{0.17em}}}$ that is used to indicate an nth root. |
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index | The positive integer n in the notation $\sqrt[n]{\text{\hspace{0.17em}}}$ that is used to indicate an nth root. |
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index | The positive integer n in the notation $\sqrt[n]{\text{\hspace{0.17em}}}$ that is used to indicate an nth root. |
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index | The positive integer n in the notation $\sqrt[n]{\text{\hspace{0.17em}}}$ that is used to indicate an nth root. |
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index of summation | The variable used in sigma notation to indicate the lower and upper bounds of the summation. | ||||

index of summation | The variable used in sigma notation to indicate the lower and upper bounds of the summation. | ||||

infinite sequence | A sequence whose domain is the set of natural numbers $\left\{1,2,3,\mathrm{\dots}\right\}.$ | ||||

infinite sequence | A sequence whose domain is the set of natural numbers $\left\{1,2,3,\mathrm{\dots}\right\}.$ | ||||

infinity | The symbol ∞ indicates the interval is unbounded to the right. | ||||

infinity | The symbol ∞ indicates the interval is unbounded to the right. | ||||

integers | The set of positive and negative whole numbers combined with zero: {…, −3, −2, −1, 0, 1, 2, 3, …}. | ||||

integers | The set of positive and negative whole numbers combined with zero: {…, −3, −2, −1, 0, 1, 2, 3, …}. | ||||

interpolation | Using a linear function to estimate a value between given data points. | ||||

interpolation | Using a linear function to estimate a value between given data points. | ||||

intersection | The set formed by the shared values of the individual solution sets that is indicated by the logical use of the word “and,” denoted with the symbol $\cap .$ | ||||

intersection | The set formed by the shared values of the individual solution sets that is indicated by the logical use of the word “and,” denoted with the symbol $\cap .$ | ||||

inverse properties of the logarithm | Given $b>0$ we have ${}_{}$ |
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inverse properties of the logarithm | Given $b>0$ we have ${}_{}$ |
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inversely proportional | Used when referring to inverse variation. | ||||

inversely proportional | Used when referring to inverse variation. | ||||

Irrational numbers | Numbers that cannot be written as a ratio of two integers. | ||||

Irrational numbers | Numbers that cannot be written as a ratio of two integers. | ||||

joint variation | Describes a quantity y that varies directly as the product of two other quantities x and z: $y=$ |
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joint variation | Describes a quantity y that varies directly as the product of two other quantities x and z: $y=$ |
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leading coefficient | The coefficient of the term with the largest degree. | ||||

least common denominator | The least common multiple of a set of denominators. | ||||

least common denominator | The least common multiple of a set of denominators. | ||||

linear equation with one variable | An equation that can be written in the standard form $ax+b=0$, where a and b are real numbers and $a\ne 0.$ |
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linear equation with one variable | An equation that can be written in the standard form $ax+b=0$, where a and b are real numbers and $a\ne 0.$ |
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linear function | Any function that can be written in the form $f\left(x\right)=mx+b$ | ||||

linear function | Any function that can be written in the form $f\left(x\right)=mx+b$ | ||||

linear inequality | Linear expressions related with the symbols $\le $, <, $\ge $, and >. | ||||

linear inequality | Linear expressions related with the symbols $\le $, <, $\ge $, and >. | ||||

linear inequality with two variables | An inequality relating linear expressions with two variables. The solution set is a region defining half of the plane. | ||||

linear inequality with two variables | An inequality relating linear expressions with two variables. The solution set is a region defining half of the plane. | ||||

linear systems | A set of two or more linear equations with the same variables. | ||||

linear systems | A set of two or more linear equations with the same variables. | ||||

logarithm base b |
The exponent to which the base b is raised in order to obtain a specific value. In other words, $y={}_{}$ |
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logarithm base b |
The exponent to which the base b is raised in order to obtain a specific value. In other words, $y={}_{}$ |
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logarithmic equation | An equation that involves a logarithm with a variable argument. | ||||

logarithmic equation | An equation that involves a logarithm with a variable argument. | ||||

mathematical modeling | Using data to find mathematical equations that describe, or model, real-world applications. | ||||

mathematical modeling | Using data to find mathematical equations that describe, or model, real-world applications. | ||||

midpoint | Given two points $\left({x}_{1},\text{\hspace{0.17em}}{y}_{1}\right)$ and $\left({x}_{2},\text{\hspace{0.17em}}{y}_{2}\right)$, the midpoint is an ordered pair given by $(\frac{{x}_{1}+}{}$ |
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midpoint | Given two points $\left({x}_{1},\text{\hspace{0.17em}}{y}_{1}\right)$ and $\left({x}_{2},\text{\hspace{0.17em}}{y}_{2}\right)$, the midpoint is an ordered pair given by $(\frac{{x}_{1}+}{}$ |
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minor | The determinant of the matrix that results after eliminating a row and column of a square matrix. | ||||

minor | The determinant of the matrix that results after eliminating a row and column of a square matrix. | ||||

monomial | Polynomial with one term. | ||||

natural logarithm | The logarithm base e, denoted $\mathrm{ln}\text{\hspace{0.17em}}x.$ |
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natural logarithm | The logarithm base e, denoted $\mathrm{ln}\text{\hspace{0.17em}}x.$ |
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negative exponents | ${x}^{-n}=\frac{}{}$n, where x is nonzero. |
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negative exponents | ${x}^{-n}=\frac{}{}$n, where x is nonzero. |
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negative infinity | The symbol −∞ indicates the interval is unbounded to the left. | ||||

negative infinity | The symbol −∞ indicates the interval is unbounded to the left. | ||||

non-rigid transformation | A set of operations that change the size and/or shape of a graph in a coordinate plane. | ||||

non-rigid transformation | A set of operations that change the size and/or shape of a graph in a coordinate plane. | ||||

nonlinear system | A system of equations where at least one equation is not linear. | ||||

nonlinear system | A system of equations where at least one equation is not linear. | ||||

nth partial sum of a geometric sequence |
The sum of the first n terms of a geometric sequence, given by the formula: ${S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r}$, $r\ne 1.$ |
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nth partial sum of a geometric sequence |
The sum of the first n terms of a geometric sequence, given by the formula: ${S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r}$, $r\ne 1.$ |
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nth partial sum of an arithmetic sequence |
The sum of the first n terms of an arithmetic sequence given by the formula: ${S}_{n}=\frac{n\left({a}_{1}+{a}_{n}\right)}{2}.$ |
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nth partial sum of an arithmetic sequence |
The sum of the first n terms of an arithmetic sequence given by the formula: ${S}_{n}=\frac{n\left({a}_{1}+{a}_{n}\right)}{2}.$ |
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nth root |
A number that when raised to the nth power $(n\ge 2)$ yields the original number. |
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nth root |
A number that when raised to the nth power $(n\ge 2)$ yields the original number. |
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odd integers | Nonzero integers that are not divisible by 2. | ||||

odd integers | Nonzero integers that are not divisible by 2. | ||||

one-to-one property of exponential functions | Given $b>0$ and $b\ne 1$ we have ${b}^{x}={b}^{y}$ if and only if $x=y.$ | ||||

one-to-one property of exponential functions | Given $b>0$ and $b\ne 1$ we have ${b}^{x}={b}^{y}$ if and only if $x=y.$ | ||||

one-to-one property of logarithms | Given $b>0$ and $b\ne 1$ where $x,y>0$ we have ${}_{}$ |
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one-to-one property of logarithms | Given $b>0$ and $b\ne 1$ where $x,y>0$ we have ${}_{}$ |
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opposite | Real numbers whose graphs are on opposite sides of the origin with the same distance to the origin. | ||||

opposite | Real numbers whose graphs are on opposite sides of the origin with the same distance to the origin. | ||||

opposite binomial property | If given a binomial $a-b$, then the opposite is $-\left(a-b\right)=b-a.$ | ||||

opposite binomial property | If given a binomial $a-b$, then the opposite is $-\left(a-b\right)=b-a.$ | ||||

opposite reciprocals | Two real numbers whose product is −1. Given a real number $\frac{a}{b}$, the opposite reciprocal is $-\frac{b}{a}.$ | ||||

opposite reciprocals | Two real numbers whose product is −1. Given a real number $\frac{a}{b}$, the opposite reciprocal is $-\frac{b}{a}.$ | ||||

ordered triple | Triples (x, y, z) that identify position relative to the origin in three-dimensional space. |
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ordered triple | Triples (x, y, z) that identify position relative to the origin in three-dimensional space. |
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origin | The point on the number line that represents zero. | ||||

origin | The point on the number line that represents zero. | ||||

origin | The point where the x- and y-axes cross, denoted by (0, 0). |
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origin | The point where the x- and y-axes cross, denoted by (0, 0). |
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parabola | The curved graph formed by the squaring function. | ||||

parabola | The curved graph formed by the squaring function. | ||||

parabola | The U-shaped graph of any quadratic function defined by $f\left(x\right)=$a, b, and c are real numbers and $a\ne 0.$ |
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parabola | The U-shaped graph of any quadratic function defined by $f\left(x\right)=$a, b, and c are real numbers and $a\ne 0.$ |
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parabola | The set of points in a plane equidistant from a given line, called the directrix, and a point not on the line, called the focus. | ||||

parabola | The set of points in a plane equidistant from a given line, called the directrix, and a point not on the line, called the focus. | ||||

parabola in standard form | The equation of a parabola written in the form $y=a{\left(x-h\right)}^{2}+k$ or $x=a{\left(y-k\right)}^{2}+h.$ | ||||

parabola in standard form | The equation of a parabola written in the form $y=a{\left(x-h\right)}^{2}+k$ or $x=a{\left(y-k\right)}^{2}+h.$ | ||||

parallel lines | Lines in the same plane that do not intersect; their slopes are the same. | ||||

parallel lines | Lines in the same plane that do not intersect; their slopes are the same. | ||||

partial sum | The sum of the first n terms in a sequence denoted ${S}_{n}.$ |
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partial sum | The sum of the first n terms in a sequence denoted ${S}_{n}.$ |
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Pascal’s triangle | A triangular array of numbers that correspond to the binomial coefficients. | ||||

Pascal’s triangle | A triangular array of numbers that correspond to the binomial coefficients. | ||||

perfect square trinomials | The trinomials obtained by squaring the binomials ${\left(a+b\right)}^{2}={a}^{2}+$ |
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perfect square trinomials | The trinomials obtained by squaring the binomials ${\left(a+b\right)}^{2}={a}^{2}+$ |
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piecewise definition | A definition that changes depending on the value of the variable. | ||||

piecewise definition | A definition that changes depending on the value of the variable. | ||||

placeholders | Terms with zero coefficients used to fill in all missing exponents within a polynomial. | ||||

placeholders | Terms with zero coefficients used to fill in all missing exponents within a polynomial. | ||||

plane | Any flat two-dimensional surface. | ||||

plane | Any flat two-dimensional surface. | ||||

plotting points | A way of determining a graph using a finite number of representative ordered pair solutions. | ||||

plotting points | A way of determining a graph using a finite number of representative ordered pair solutions. | ||||

point-slope form | Any nonvertical line can be written in the form $y-{y}_{1}=\text{\hspace{0.17em}}m\left(x-{x}_{1}\right)$, where m is the slope and $({x}_{1},\hspace{0.17em}{y}_{1})$ is any point on the line. |
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point-slope form | Any nonvertical line can be written in the form $y-{y}_{1}=\text{\hspace{0.17em}}m\left(x-{x}_{1}\right)$, where m is the slope and $({x}_{1},\hspace{0.17em}{y}_{1})$ is any point on the line. |
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polynomial | An algebraic expression consisting of terms with real number coefficients and variables with whole number exponents. | ||||

polynomial | An algebraic expression consisting of terms with real number coefficients and variables with whole number exponents. | ||||

polynomial inequality | A mathematical statement that relates a polynomial expression as either less than or greater than another. | ||||

polynomial inequality | A mathematical statement that relates a polynomial expression as either less than or greater than another. | ||||

polynomial long division | The process of dividing two polynomials using the division algorithm. | ||||

polynomial long division | The process of dividing two polynomials using the division algorithm. | ||||

polynomials with one variable | A polynomial where each term has the form $$n is any whole number. |
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polynomials with one variable | A polynomial where each term has the form $$n is any whole number. |
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power property of equality | Given any positive integer n and real numbers a and b where $a=b$, then ${a}^{n}={b}^{n}.$ |
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power property of equality | Given any positive integer n and real numbers a and b where $a=b$, then ${a}^{n}={b}^{n}.$ |
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power property of logarithms | ${}_{}$ |
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power property of logarithms | ${}_{}$ |
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power rule for exponents | ${\left({x}^{m}\right)}^{n}={}^{}$ |
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power rule for exponents | ${\left({x}^{m}\right)}^{n}={}^{}$ |
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prime factorization | The unique factorization of a natural number written as a product of primes. | ||||

prime factorization | The unique factorization of a natural number written as a product of primes. | ||||

prime number | Integer greater than 1 that is divisible only by 1 and itself. | ||||

prime number | Integer greater than 1 that is divisible only by 1 and itself. | ||||

prime polynomial | A polynomial with integer coefficients that cannot be factored as a product of polynomials with integer coefficients other than 1 and itself. | ||||

prime polynomial | A polynomial with integer coefficients that cannot be factored as a product of polynomials with integer coefficients other than 1 and itself. | ||||

principal (nonnegative) nth root |
The positive nth root when n is even. |
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principal (nonnegative) nth root |
The positive nth root when n is even. |
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principal (nonnegative) square root | The non-negative square root. | ||||

principal (nonnegative) square root | The non-negative square root. | ||||

principal (nonnegative) square root | The positive square root of a positive real number, denoted with the symbol $\sqrt{\text{\hspace{0.17em}}}.$ | ||||

principal (nonnegative) square root | The positive square root of a positive real number, denoted with the symbol $\sqrt{\text{\hspace{0.17em}}}.$ | ||||

product of complex conjugates | The real number that results from multiplying complex conjugates: $\left(a+bi\right)\left(a-bi\right)={a}^{2}+{b}^{2}.$ | ||||

product of complex conjugates | The real number that results from multiplying complex conjugates: $\left(a+bi\right)\left(a-bi\right)={a}^{2}+{b}^{2}.$ | ||||

product property of logarithms | ${}_{}$ |
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product property of logarithms | ${}_{}$ |
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product rule for exponents | ${x}^{m}\cdot {x}^{n}={x}^{m+n}$; the product of two expressions with the same base can be simplified by adding the exponents. | ||||

product rule for exponents | ${x}^{m}\cdot {x}^{n}={x}^{m+n}$; the product of two expressions with the same base can be simplified by adding the exponents. | ||||

profit function | A function that models the profit as revenue less cost. | ||||

profit function | A function that models the profit as revenue less cost. | ||||

properties of equality | Properties that allow us to obtain equivalent equations by adding, subtracting, multiplying, and dividing both sides of an equation by nonzero real numbers. | ||||

properties of equality | Properties that allow us to obtain equivalent equations by adding, subtracting, multiplying, and dividing both sides of an equation by nonzero real numbers. | ||||

properties of inequalities | Properties used to obtain equivalent inequalities and used as a means to solve them. | ||||

properties of inequalities | Properties used to obtain equivalent inequalities and used as a means to solve them. | ||||

proportion | A statement of equality of two ratios. | ||||

proportion | A statement of equality of two ratios. | ||||

Pythagorean theorem | The hypotenuse of any right triangle is equal to the square root of the sum of the squares of the lengths of the triangle’s legs. | ||||

Pythagorean theorem | The hypotenuse of any right triangle is equal to the square root of the sum of the squares of the lengths of the triangle’s legs. | ||||

quadrants | The four regions of a rectangular coordinate plane partly bounded by the x- and y-axes and numbered using the Roman numerals I, II, III, and IV. |
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quadrants | The four regions of a rectangular coordinate plane partly bounded by the x- and y-axes and numbered using the Roman numerals I, II, III, and IV. |
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quadratic form | An equation of the form $$a, b and c are real numbers and u represents an algebraic expression. |
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quadratic form | An equation of the form $$a, b and c are real numbers and u represents an algebraic expression. |
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quadratic formula | The formula $x=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}$, which gives the solutions to any quadratic equation in the standard form $$a, b, and c are real numbers and $a\ne 0.$ |
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quadratic formula | The formula $x=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}$, which gives the solutions to any quadratic equation in the standard form $$a, b, and c are real numbers and $a\ne 0.$ |
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quadratic inequality | A mathematical statement that relates a quadratic expression as either less than or greater than another. | ||||

quadratic inequality | A mathematical statement that relates a quadratic expression as either less than or greater than another. | ||||

quotient | The result of division. | ||||

quotient | The result of dividing. | ||||

quotient | The result of division. | ||||

quotient | The result of dividing. | ||||

quotient property of logarithms | ${}_{}$ |
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quotient property of logarithms | ${}_{}$ |
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quotient rule for radicals | Given real numbers $\sqrt[n]{A}$ and $\sqrt[n]{B}$, $\text{\hspace{0.17em}}\text{exception 25:}$ |
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quotient rule for radicals | Given real numbers $\sqrt[n]{A}$ and $\sqrt[n]{B}$, $\text{\hspace{0.17em}}\text{exception 25:}$ |
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quotients with negative exponents | $\frac{{x}^{-n}}{{y}^{-m}}=\frac{}{}$m and n, where $x\ne 0\hspace{0.17em}$ and $y\ne 0.$ |
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quotients with negative exponents | $\frac{{x}^{-n}}{{y}^{-m}}=\frac{}{}$m and n, where $x\ne 0\hspace{0.17em}$ and $y\ne 0.$ |
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radical | Used when referring to an expression of the form $\sqrt[n]{A}.$ | ||||

radical | Used when referring to an expression of the form $\sqrt[n]{A}.$ | ||||

radical equation | Any equation that contains one or more radicals with a variable in the radicand. | ||||

radical equation | Any equation that contains one or more radicals with a variable in the radicand. | ||||

radical expression | An algebraic expression that contains radicals. | ||||

radical expression | An algebraic expression that contains radicals. | ||||

radical is simplified | A radical where the radicand does not consist of any factors that can be written as perfect powers of the index. | ||||

radical is simplified | A radical where the radicand does not consist of any factors that can be written as perfect powers of the index. | ||||

radicand | The number within a radical. | ||||

radicand | The number within a radical. | ||||

radicand | The expression A within a radical sign, $\sqrt[n]{A}.$ |
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radicand | The expression A within a radical sign, $\sqrt[n]{A}.$ |
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rational equation | An equation containing at least one rational expression. | ||||

rational equation | An equation containing at least one rational expression. | ||||

rational inequality | A mathematical statement that relates a rational expression as either less than or greater than another. | ||||

rational inequality | A mathematical statement that relates a rational expression as either less than or greater than another. | ||||

rationalizing the denominator | The process of determining an equivalent radical expression with a rational denominator. | ||||

rationalizing the denominator | The process of determining an equivalent radical expression with a rational denominator. | ||||

real numbers | The set of all rational and irrational numbers. | ||||

real numbers | The set of all rational and irrational numbers. | ||||

reciprocal function | The function defined by $f(x)=\frac{1}{x}.$ | ||||

reciprocal function | The function defined by $f(x)=\frac{1}{x}.$ | ||||

reciprocals | Two real numbers whose product is 1. | ||||

reciprocals | Two real numbers whose product is 1. | ||||

recurrence relation | A formula that uses previous terms of a sequence to describe subsequent terms. | ||||

recurrence relation | A formula that uses previous terms of a sequence to describe subsequent terms. | ||||

reducing | The process of finding equivalent fractions by dividing the numerator and the denominator by common factors. | ||||

reducing | The process of finding equivalent fractions by dividing the numerator and the denominator by common factors. | ||||

reflection | A transformation that produces a mirror image of the graph about an axis. | ||||

reflection | A transformation that produces a mirror image of the graph about an axis. | ||||

relation | Any set of ordered pairs. | ||||

relation | Any set of ordered pairs. | ||||

relatively prime | Expressions that share no common factors other than 1. | ||||

relatively prime | Expressions that share no common factors other than 1. | ||||

Restrictions | The set of real numbers for which a rational function is not defined. | ||||

Restrictions | The set of real numbers for which a rational function is not defined. | ||||

revenue function | A function that models income based on a number of units sold. | ||||

revenue function | A function that models income based on a number of units sold. | ||||

root | A value in the domain of a function that results in zero. | ||||

root | A value in the domain of a function that results in zero. | ||||

row echelon form | A matrix in triangular form where the leading nonzero element of each row is 1. | ||||

row echelon form | A matrix in triangular form where the leading nonzero element of each row is 1. | ||||

run | The horizontal change between any two points on a line. | ||||

run | The horizontal change between any two points on a line. | ||||

scientific notation | Real numbers expressed the form $$n is an integer and $1\le a<10.$ |
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scientific notation | Real numbers expressed the form $$n is an integer and $1\le a<10.$ |
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secant line | Line that intersects two points on the graph of a function. | ||||

secant line | Line that intersects two points on the graph of a function. | ||||

set notation | Notation used to describe a set using mathematical symbols. | ||||

set notation | Notation used to describe a set using mathematical symbols. | ||||

sign chart | A model of a function using a number line and signs (+ or −) to indicate regions in the domain where the function is positive or negative. | ||||

sign chart | A model of a function using a number line and signs (+ or −) to indicate regions in the domain where the function is positive or negative. | ||||

similar radicals | Term used when referring to like radicals. | ||||

similar radicals | Term used when referring to like radicals. | ||||

similar terms | Used when referring to like terms. | ||||

similar terms | Used when referring to like terms. | ||||

Simple interest | Modeled by the formula $I=$p represents the principal amount invested at an annual interest rate r for t years. |
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Simple interest | Modeled by the formula $I=$p represents the principal amount invested at an annual interest rate r for t years. |
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simplified radical | A radical where the radicand does not consist of any factors that can be written as perfect powers of the index. | ||||

simplified radical | |||||

simplifying the expression | The process of combining like terms until the expression contains no more similar terms. | ||||

simplifying the expression | The process of combining like terms until the expression contains no more similar terms. | ||||

simultaneous solution | Used when referring to a solution of a system of equations. | ||||

simultaneous solution | Used when referring to a solution of a system of equations. | ||||

slope formula | The slope of the line through the points $\left({x}_{1},{y}_{1}\right)$ and $\left({x}_{2},{y}_{2}\right)$ is given by the formula $m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}.$ | ||||

slope formula | The slope of the line through the points $\left({x}_{1},{y}_{1}\right)$ and $\left({x}_{2},{y}_{2}\right)$ is given by the formula $m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}.$ | ||||

slope-intercept form | Any nonvertical line can be written in the form $y=mx+b$, where m is the slope and (0, b) is the y-intercept. |
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slope-intercept form | Any nonvertical line can be written in the form $y=mx+b$, where m is the slope and (0, b) is the y-intercept. |
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solution | Any value that can replace the variable in an equation to produce a true statement. | ||||

solution | Any value that can replace the variable in an equation to produce a true statement. | ||||

solution to a linear inequality | A real number that produces a true statement when its value is substituted for the variable. | ||||

solution to a linear inequality | A real number that produces a true statement when its value is substituted for the variable. | ||||

Solutions | Values that can be used in place of the variable to satisfy the given condition. | ||||

Solutions | Values that can be used in place of the variable to satisfy the given condition. | ||||

solve by factoring | The process of solving an equation that is equal to zero by factoring it and then setting each variable factor equal to zero. | ||||

solve by factoring | The process of solving an equation that is equal to zero by factoring it and then setting each variable factor equal to zero. | ||||

split function | A term used when referring to a piecewise function. | ||||

split function | A term used when referring to a piecewise function. | ||||

square matrix | A matrix with the same number of rows and columns. | ||||

square matrix | A matrix with the same number of rows and columns. | ||||

square root function | The function defined by $f(x)=\sqrt{x}.$ | ||||

square root function | The function defined by $f(x)=\sqrt{x}.$ | ||||

square root function | The function defined by $f\left(x\right)=\sqrt{x}.$ | ||||

square root function | The function defined by $f\left(x\right)=\sqrt{x}.$ | ||||

square root property | For any real number k, if ${x}^{2}=k$, then $x=\pm \sqrt{k}.$ |
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square root property | For any real number k, if ${x}^{2}=k$, then $x=\pm \sqrt{k}.$ |
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squaring function | The quadratic function defined by $f(x)={x}^{2}.$ | ||||

squaring function | The quadratic function defined by $f(x)={x}^{2}.$ | ||||

squaring property of equality | Given real numbers a and b, where $a=b$, then ${a}^{2}={b}^{2}.$ |
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squaring property of equality | Given real numbers a and b, where $a=b$, then ${a}^{2}={b}^{2}.$ |
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standard form | Any quadratic equation in the form $$a, b, and c are real numbers and $a\ne 0.$ |
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standard form | Any quadratic equation in the form $$a, b, and c are real numbers and $a\ne 0.$ |
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substitute | The act of replacing a variable with an equivalent quantity. | ||||

substitute | The act of replacing a variable with an equivalent quantity. | ||||

substitution method | A means of solving a linear system by solving for one of the variables and substituting the result into the other equation. | ||||

substitution method | A means of solving a linear system by solving for one of the variables and substituting the result into the other equation. | ||||

subtraction | Subtract functions as indicated by the notation: $\left(f-g\right)\left(x\right)=f\left(x\right)-g\left(x\right).$ | ||||

subtraction | Subtract functions as indicated by the notation: $\left(f-g\right)\left(x\right)=f\left(x\right)-g\left(x\right).$ | ||||

sum of squares | ${a}^{2}+{b}^{2},$ where a and b represent algebraic expressions. This does not have a general factored equivalent. |
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sum of squares | ${a}^{2}+{b}^{2},$ where a and b represent algebraic expressions. This does not have a general factored equivalent. |
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summation | Used when referring to sigma notation. | ||||

summation | Used when referring to sigma notation. | ||||

symmetric property | Allows you to solve for the variable on either side of the equal sign, because $x=5$ is equivalent to $5=x.$ | ||||

symmetric property | Allows you to solve for the variable on either side of the equal sign, because $x=5$ is equivalent to $5=x.$ | ||||

system of inequalities | A set of two or more inequalities with the same variables. | ||||

system of inequalities | A set of two or more inequalities with the same variables. | ||||

TBA | Given any real number a, $a+0=0+a=a\hspace{0.17em}.$ |
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TBA | Given any real number a, $a+\left(-a\right)=\left(-a\right)+a=0.$ |
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TBA | Given real numbers a, b and c, $\left(a+b\right)+c=a+\left(b+c\right).$ |
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TBA | Given real numbers a and b, $a+b=b+a.$ |
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TBA | Given any real number a, $a\cdot 0=0\cdot a=0\hspace{0.17em}.$ |
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TBA | Given any real number a, $a\cdot 1=1\cdot a=a\hspace{0.17em}.$ |
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TBA | Given any real numbers a, b and c, $\left(a\cdot b\right)\cdot c=a\cdot \left(b\cdot c\right).$ |
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TBA | Given any real numbers a and b, $a\cdot b=b\cdot a.$ |
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TBA | Given real numbers $\sqrt[n]{A}$ and $\sqrt[n]{B}$, $\text{\hspace{0.17em}}\sqrt[n]{A\cdot B}=\sqrt[n]{A}\cdot \sqrt[n]{B}.$ | ||||

TBA | Given real numbers $\sqrt[n]{A}$ and $\sqrt[n]{B}$, $\text{\hspace{0.17em}}\text{exception 25:}$ |
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TBA | ${\left(xy\right)}^{n}=$ |
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TBA | ${\left(\frac{x}{y}\right)}^{n}=\frac{}{}$ |
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TBA | $\frac{}{}$ |
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TBA | A polynomial with degree 1. | ||||

TBA | A polynomial with degree 2. | ||||

TBA | A polynomial with degree 3. | ||||

TBA | Given any real number a, $a+0=0+a=a\hspace{0.17em}.$ |
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TBA | Given any real number a, $a+\left(-a\right)=\left(-a\right)+a=0.$ |
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TBA | Given real numbers a, b and c, $\left(a+b\right)+c=a+\left(b+c\right).$ |
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TBA | Given real numbers a and b, $a+b=b+a.$ |
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TBA | Given any real number a, $a\cdot 0=0\cdot a=0\hspace{0.17em}.$ |
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TBA | Given any real number a, $a\cdot 1=1\cdot a=a\hspace{0.17em}.$ |
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TBA | Given any real numbers a, b and c, $\left(a\cdot b\right)\cdot c=a\cdot \left(b\cdot c\right).$ |
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TBA | Given any real numbers a and b, $a\cdot b=b\cdot a.$ |
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TBA | Given real numbers $\sqrt[n]{A}$ and $\sqrt[n]{B}$, $\text{\hspace{0.17em}}\sqrt[n]{A\cdot B}=\sqrt[n]{A}\cdot \sqrt[n]{B}.$ | ||||

TBA | Given real numbers $\sqrt[n]{A}$ and $\sqrt[n]{B}$, $\text{\hspace{0.17em}}\text{exception 25:}$ |
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TBA | ${\left(xy\right)}^{n}=$ |
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TBA | ${\left(\frac{x}{y}\right)}^{n}=\frac{}{}$ |
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TBA | $\frac{}{}$ |
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TBA | Used when referring to direct variation. | ||||

TBA | Used when referring to joint variation. | ||||

TBA | Used when referring to direct variation. | ||||

TBA | Used when referring to joint variation. | ||||

test points | A point not on the boundary of the linear inequality used as a means to determine in which half-plane the solutions lie. | ||||

test points | A point not on the boundary of the linear inequality used as a means to determine in which half-plane the solutions lie. | ||||

trial and error (or guess and check) method | Describes the method of factoring a trinomial by systematically checking factors to see if their product is the original trinomial. | ||||

trial and error (or guess and check) method | Describes the method of factoring a trinomial by systematically checking factors to see if their product is the original trinomial. | ||||

trinomial | Polynomial with three terms. | ||||

u-substitution |
A technique in algebra using substitution to transform equations into familiar forms. | ||||

u-substitution |
A technique in algebra using substitution to transform equations into familiar forms. | ||||

undefined | A quotient such as $\frac{5}{0}$ is left without meaning and is not assigned an interpretation. | ||||

undefined | A quotient such as $\frac{5}{0}$ is left without meaning and is not assigned an interpretation. | ||||

uniform motion | The distance D after traveling at an average rate r for some time t can be calculated using the formula $D=rt.$ |
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uniform motion | The distance D after traveling at an average rate r for some time t can be calculated using the formula $D=rt.$ |
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Uniform motion (or distance) | Described by the formula $D=rt$, where the distance D is given as the product of the average rate r and the time t traveled at that rate. |
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Uniform motion (or distance) | Described by the formula $D=rt$, where the distance D is given as the product of the average rate r and the time t traveled at that rate. |
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union | The set formed by joining the individual solution sets indicated by the logical use of the word “or” and denoted with the symbol $\cup .$ | ||||

union | The set formed by joining the individual solution sets indicated by the logical use of the word “or” and denoted with the symbol $\cup .$ | ||||

unit circle | The circle centered at the origin with radius 1; its equation is ${x}^{2}+{y}^{2}=1.$ | ||||

unit circle | The circle centered at the origin with radius 1; its equation is ${x}^{2}+{y}^{2}=1.$ | ||||

upper triangular form | A linear system consisting of equations with three variables in standard form arranged so that the variable x does not appear after the first equation and the variable y does not appear after the second equation. |
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upper triangular form | A linear system consisting of equations with three variables in standard form arranged so that the variable x does not appear after the first equation and the variable y does not appear after the second equation. |
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variables | Letters used to represent numbers. | ||||

variables | Letters used to represent numbers. | ||||

vertex form | A quadratic function written in the form $f\left(x\right)=a{\left(x-h\right)}^{2}+k.$ | ||||

vertex form | A quadratic function written in the form $f\left(x\right)=a{\left(x-h\right)}^{2}+k.$ | ||||

vertex form | The equation of a parabola written in standard form is often called vertex form. In this form the vertex is apparent: $\left(h,k\right).$ | ||||

vertex form | The equation of a parabola written in standard form is often called vertex form. In this form the vertex is apparent: $\left(h,k\right).$ | ||||

vertical asymptote | A vertical line to which a graph becomes infinitely close. | ||||

vertical asymptote | A vertical line to which a graph becomes infinitely close. | ||||

vertical line test | If any vertical line intersects the graph more than once, then the graph does not represent a function. | ||||

vertical line test | If any vertical line intersects the graph more than once, then the graph does not represent a function. | ||||

vertical translation | A rigid transformation that shifts a graph up or down. | ||||

vertical translation | A rigid transformation that shifts a graph up or down. | ||||

vertices. | Points on the separate branches of a hyperbola where the distance is a minimum. | ||||

vertices. | Points on the separate branches of a hyperbola where the distance is a minimum. | ||||

whole numbers | The set of natural numbers combined with zero: {0, 1, 2, 3, 4, 5, …}. | ||||

whole numbers | The set of natural numbers combined with zero: {0, 1, 2, 3, 4, 5, …}. | ||||

work rate | The rate at which a task can be performed. | ||||

work rate | The rate at which a task can be performed. | ||||

work-rate formula | $\frac{1}{{t}_{1}}\cdot t+\frac{1}{{t}_{2}}\cdot t=1$, where $\frac{}{}$t is the time it takes to complete the task working together. |
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work-rate formula | $\frac{1}{{t}_{1}}\cdot t+\frac{1}{{t}_{2}}\cdot t=1$, where $\frac{}{}$t is the time it takes to complete the task working together. |
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x-intercept |
The point (or points) where a graph intersects the x-axis, expressed as an ordered pair (x, 0). |
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x-intercept |
The point (or points) where a graph intersects the x-axis, expressed as an ordered pair (x, 0). |
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y-intercept |
The point (or points) where a graph intersects the y-axis, expressed as an ordered pair (0, y). |
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y-intercept |
The point (or points) where a graph intersects the y-axis, expressed as an ordered pair (0, y). |
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zero as an exponent | ${x}^{0}=1\hspace{0.17em}$; any nonzero base raised to the 0 power is defined to be 1. | ||||

zero as an exponent | ${x}^{0}=1\hspace{0.17em}$; any nonzero base raised to the 0 power is defined to be 1. | ||||

zero factorial | The factorial of zero is defined to be equal to 1; $0!=1.$ | ||||

zero factorial | The factorial of zero is defined to be equal to 1; $0!=1.$ | ||||

zero-product property | A product is equal to zero if and only if at least one of the factors is zero. | ||||

zero-product property | A product is equal to zero if and only if at least one of the factors is zero. |