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Mathematics LibreTexts

Glossary

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    Glossary Entries
    Word(s) Definition Image Caption Link Source
      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 |a|.        
    absolute value function The function defined by f(x)=|x|.        
    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.        
    addition property of equations If A, B, C, and D are algebraic expressions, where A = B and C = D, then A + C = B + D.        
    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 C–(x)=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 C–(x)=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: (nk)=n!k!(n−k)!.        
    binomial coefficient An integer that is calculated using the formula: (nk)=n!k!(n−k)!.        
    binomial theorem Describes the algebraic expansion of binomials raised to powers: (x+y)n= Σk=0n (nk) xn−kyk.        
    binomial theorem Describes the algebraic expansion of binomials raised to powers: (x+y)n= Σk=0n (nk) xn−kyk.        
    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 loga x=logb xlogb a; we can write any base-a logarithm in terms of base-b logarithms using this formula.        
    change of base formula loga x=logb xlogb a; we can write any base-a logarithm in terms of base-b logarithms using this formula.        
    circle in general form The equation of a circle written in the form x2+y2+cx+dy+e=0.        
    circle in general form The equation of a circle written in the form x2+y2+cx+dy+e=0.        
    circle in standard form The equation of a circle written in the form (x−h)2+(y−k)2=r2 where (h,k) is the center and r is the radius.        
    circle in standard form The equation of a circle written in the form (x−h)2+(y−k)2=r2 where (h,k) is the center and r is the radius.        
    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; an−an−1=d.        
    common difference The constant d that is obtained from subtracting any two successive terms of an arithmetic sequence; an−an−1=d.        
    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 log x.        
    common logarithm The logarithm base 10, denoted log x.        
    common ratio The constant r that is obtained from dividing any two successive terms of a geometric sequence; anan−1=r.        
    common ratio The constant r that is obtained from dividing any two successive terms of a geometric sequence; anan−1=r.        
    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 (x−p)2=q.        
    completing the square The process of rewriting a quadratic equation to be in the form (x−p)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 (f○g)(x)=f(g(x)).        
    composition operator The open dot used to indicate the function composition (f○g)(x)=f(g(x)).        
    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(t)=P(1+rn)nt.        
    compound interest formula A formula that gives the amount accumulated by earning interest on principal and interest over time: A(t)=P(1+rn)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 (a+b) and (a−b).        
    conjugate binomials The binomials (a+b) and (a−b).        
    conjugates The factors (a+b) and (a−b) are conjugates.        
    conjugates The factors (a+b) and (a−b) are conjugates.        
    constant function Any function of the form f(x)=c where c is a real number.        
    constant function Any function of the form f(x)=c where c is a real number.        
    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.        
    constant of variation The nonzero multiple k, when quantities vary directly or inversely.        
    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(t)=Pert.        
    continuously compounding interest formula A formula that gives the amount accumulated by earning continuously compounded interest: A(t)=Pert.        
    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 |r|<1 whose sum is given by the formula: S∞=a11−r.        
    convergent geometric series An infinite geometric series where |r|<1 whose sum is given by the formula: S∞=a11−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  ab=cd then ad=bc.        
    cross multiplication If  ab=cd 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(x)=x3.        
    cube root function The function defined by f(x)=x3.        
    cubing function The cubic function defined by f(x)=x3.        
    cubing function The cubic function defined by f(x)=x3.        
    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 (x,mx+b).        
    dependent system A linear system with two variables that consists of equivalent equations. It has infinitely many ordered pair solutions, denoted by (x,mx+b).        
    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.        
    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.        
    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 a3−b3=(a−b)(a2+ab+b2), where a and b represent algebraic expressions.        
    difference of cubes a3−b3=(a−b)(a2+ab+b2), where a and b represent algebraic expressions.        
    difference of squares The special product obtained by multiplying conjugate binomials (a+b)(a−b)=a2−b2.        
    difference of squares The special product obtained by multiplying conjugate binomials (a+b)(a−b)=a2−b2.        
    difference of squares a2−b2=(a+b)(a−b), where a and b represent algebraic expressions.        
    difference of squares a2−b2=(a+b)(a−b), where a and b represent algebraic expressions.        
    difference quotient The mathematical quantity f(x+h)−f(x)h, where h≠0, which represents the slope of a secant line through a function f.        
    difference quotient The mathematical quantity f(x+h)−f(x)h, where h≠0, which represents the slope of a secant line through a function f.        
    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, b2−4ac.        
    discriminant The expression inside the radical of the quadratic formula, b2−4ac.        
    distance formula Given two points (x1, y1) and (x2, y2), calculate the distance d between them using the formula d=(x2−x1)2+(y2−y1)2.        
    distance formula Given two points (x1, y1) and (x2, y2), calculate the distance d between them using the formula d=(x2−x1)2+(y2−y1)2.        
    distance formula Given two points (x1, y1) and (x2, y2), the distance d between them is given by d=(x2−x1)2+(y2−y1)2.        
    distance formula Given two points (x1, y1) and (x2, y2), the distance d between them is given by d=(x2−x1)2+(y2−y1)2.        
    distributive property Given any real numbers a, b, and c, a(b+c)=ab+ac or (b+c)a=ba+ca.        
    distributive property Given any real numbers a, b, and c, a(b+c)=ab+ac or (b+c)a=ba+ca.        
    division Divide functions as indicated by the notation: (f/g)(x)=f(x)g(x), where g(x)≠0.        
    division Divide functions as indicated by the notation: (f/g)(x)=f(x)g(x), where g(x)≠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.        
    double-negative property The opposite of a negative number is positive: −(−a) = a.        
    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 px2+qy2+cx+dy+e=0 where p,q>0.        
    ellipse in general form The equation of an ellipse written in the form px2+qy2+cx+dy+e=0 where p,q>0.        
    ellipse in standard form The equation of an ellipse written in the form (x−h)2a2+(y−k)2b2=1. The center is (h,k) and the larger of a and b is the major radius and the smaller is the minor radius.        
    ellipse in standard form The equation of an ellipse written in the form (x−h)2a2+(y−k)2b2=1. The center is (h,k) and the larger of a and b is the major radius and the smaller is the minor radius.        
    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 an that indicates the number of times the base is used as a factor.        
    exponent The positive integer n in the exponential notation an that indicates the number of times the base is used as a factor.        
    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(x)=bx where b>0 and b≠1.        
    exponential function Any function with a definition of the form f(x)=bx where b>0 and b≠1.        
    exponential growth/decay formula A formula that models exponential growth or decay: P(t)=P0ekt.        
    exponential growth/decay formula A formula that models exponential growth or decay: P(t)=P0ekt.        
    exponential notation The compact notation an used when a factor a is repeated n times.        
    exponential notation The compact notation an used when a factor a is repeated n times.        
    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!.        
    factorial The product of all natural numbers less than or equal to a given natural number, denoted n!.        
    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 {1,2,3,…,k} where k is a natural number.        
    finite sequence A sequence whose domain is {1,2,3,…,k} where k is a natural number.        
    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: ab, where b≠0.        
    fraction A rational number written as a quotient of two integers: ab, where b≠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(x)=y, which reads “f of x is equal to y.” Given a function, y and f(x) can be used interchangeably.        
    function notation The notation f(x)=y, which reads “f of x is equal to y.” Given a function, y and f(x) can be used interchangeably.        
    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 an.        
    general term of a sequence An equation that defines the nth term of a sequence commonly denoted using subscripts an.        
    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]].        
    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]].        
    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 ±∞.        
    horizontal asymptote A horizontal line to which a graph becomes infinitely close where the x-values tend toward ±∞.        
    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 px2−qy2+cx+dy+e=0 or qy2−px2−cx+dy+e=0 where p,q>0.        
    hyperbola in general form The equation of a hyperbola written in the form px2−qy2+cx+dy+e=0 or qy2−px2−cx+dy+e=0 where p,q>0.        
    hyperbola opening left and right in standard form The equation of a hyperbola written in the form (x−h)2a2−(y−k)2b2=1. The center is (h,k), a defines the transverse axis, and b defines the conjugate axis.        
    hyperbola opening left and right in standard form The equation of a hyperbola written in the form (x−h)2a2−(y−k)2b2=1. The center is (h,k), a defines the transverse axis, and b defines the conjugate axis.        
    hyperbola opening upward and downward in standard form The equation of a hyperbola written in the form (y−k)2b2−(x−h)2a2=1. The center is (h,k), b defines the transverse axis, and a defines the conjugate axis.        
    hyperbola opening upward and downward in standard form The equation of a hyperbola written in the form (y−k)2b2−(x−h)2a2=1. The center is (h,k), b defines the transverse axis, and a defines the conjugate axis.        
    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.        
    imaginary part The real number b of a complex number a+bi.        
    imaginary unit Defined as i=−1 where i2=−1.        
    imaginary unit Defined as i=−1 where i2=−1.        
    inclusive inequalities Use the symbol ≤ to express quantities that are “less than or equal to” and ≥ for quantities that are “greater than or equal to” each other.        
    inclusive inequalities Use the symbol ≤ to express quantities that are “less than or equal to” and ≥ 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 00 is a quantity that is uncertain or ambiguous.        
    indeterminate A quotient such as 00 is a quantity that is uncertain or ambiguous.        
    index The positive integer n in the notation  n that is used to indicate an nth root.        
    index The positive integer n in the notation  n that is used to indicate an nth root.        
    index The positive integer n in the notation  n that is used to indicate an nth root.        
    index The positive integer n in the notation  n that is used to indicate an nth root.        
    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 {1,2,3,…}.        
    infinite sequence A sequence whose domain is the set of natural numbers {1,2,3,…}.        
    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 ∩.        
    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 ∩.        
    inverse properties of the logarithm Given b>0 we have logb bx=x and blogb x=x when x>0.        
    inverse properties of the logarithm Given b>0 we have logb bx=x and blogb x=x when x>0.        
    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=kxz.        
    joint variation Describes a quantity y that varies directly as the product of two other quantities x and z: y=kxz.        
    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≠0.        
    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≠0.        
    linear function Any function that can be written in the form f(x)=mx+b        
    linear function Any function that can be written in the form f(x)=mx+b        
    linear inequality Linear expressions related with the symbols ≤, <, ≥, and >.        
    linear inequality Linear expressions related with the symbols ≤, <, ≥, 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=logb x is equivalent to by=x.        
    logarithm base b The exponent to which the base b is raised in order to obtain a specific value. In other words, y=logb x is equivalent to by=x.        
    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 (x1, y1) and (x2, y2), the midpoint is an ordered pair given by (x1+x22,   y1+y22).        
    midpoint Given two points (x1, y1) and (x2, y2), the midpoint is an ordered pair given by (x1+x22,   y1+y22).        
    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 ln x.        
    natural logarithm The logarithm base e, denoted ln x.        
    negative exponents x−n=1xn , given any integer n, where x is nonzero.        
    negative exponents x−n=1xn , given any integer n, where x is nonzero.        
    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: Sn=a1(1−rn)1−r, r≠1.        
    nth partial sum of a geometric sequence The sum of the first n terms of a geometric sequence, given by the formula: Sn=a1(1−rn)1−r, r≠1.        
    nth partial sum of an arithmetic sequence The sum of the first n terms of an arithmetic sequence given by the formula: Sn=n(a1+an)2.        
    nth partial sum of an arithmetic sequence The sum of the first n terms of an arithmetic sequence given by the formula: Sn=n(a1+an)2.        
    nth root A number that when raised to the nth power (n≥2) yields the original number.        
    nth root A number that when raised to the nth power (n≥2) yields the original number.        
    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≠1 we have bx=by if and only if x=y.        
    one-to-one property of exponential functions Given b>0 and b≠1 we have bx=by if and only if x=y.        
    one-to-one property of logarithms Given b>0 and b≠1 where x,y>0 we have logb x=logb y if and only if x=y.        
    one-to-one property of logarithms Given b>0 and b≠1 where x,y>0 we have logb x=logb y if and only if x=y.        
    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 −(a−b)=b−a.        
    opposite binomial property If given a binomial a−b, then the opposite is −(a−b)=b−a.        
    opposite reciprocals Two real numbers whose product is −1. Given a real number ab, the opposite reciprocal is −ba.        
    opposite reciprocals Two real numbers whose product is −1. Given a real number ab, the opposite reciprocal is −ba.        
    ordered triple Triples (x, y, z) that identify position relative to the origin in three-dimensional space.        
    ordered triple Triples (x, y, z) that identify position relative to the origin in three-dimensional space.        
    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).        
    origin The point where the x- and y-axes cross, denoted by (0, 0).        
    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(x)=ax2+bx+c, where a, b, and c are real numbers and a≠0.        
    parabola The U-shaped graph of any quadratic function defined by f(x)=ax2+bx+c, where a, b, and c are real numbers and a≠0.        
    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(x−h)2+k or x=a(y−k)2+h.        
    parabola in standard form The equation of a parabola written in the form y=a(x−h)2+k or x=a(y−k)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 Sn.        
    partial sum The sum of the first n terms in a sequence denoted Sn.        
    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 (a+b)2=a2+2ab+b2 and (a−b)2=a2−2ab+b2.        
    perfect square trinomials The trinomials obtained by squaring the binomials (a+b)2=a2+2ab+b2 and (a−b)2=a2−2ab+b2.        
    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−y1= m(x−x1), where m is the slope and (x1, y1) is any point on the line.        
    point-slope form Any nonvertical line can be written in the form y−y1= m(x−x1), where m is the slope and (x1, y1) is any point on the line.        
    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 anxn, where an is any real number and n is any whole number.        
    polynomials with one variable A polynomial where each term has the form anxn, where an is any real number and n is any whole number.        
    power property of equality Given any positive integer n and real numbers a and b where a=b, then an=bn.        
    power property of equality Given any positive integer n and real numbers a and b where a=b, then an=bn.        
    power property of logarithms logb xn=nlogb x; the logarithm of a quantity raised to a power is equal to that power times the logarithm of the quantity.        
    power property of logarithms logb xn=nlogb x; the logarithm of a quantity raised to a power is equal to that power times the logarithm of the quantity.        
    power rule for exponents (xm)n=xmn; a power raised to a power can be simplified by multiplying the exponents.        
    power rule for exponents (xm)n=xmn; a power raised to a power can be simplified by multiplying the exponents.        
    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.        
    principal (nonnegative) nth root The positive nth root when n is even.        
    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  .        
    principal (nonnegative) square root The positive square root of a positive real number, denoted with the symbol  .        
    product of complex conjugates The real number that results from multiplying complex conjugates: (a+bi)(a−bi)=a2+b2.        
    product of complex conjugates The real number that results from multiplying complex conjugates: (a+bi)(a−bi)=a2+b2.        
    product property of logarithms logb (xy)=logb x+logb y; the logarithm of a product is equal to the sum of the logarithm of the factors.        
    product property of logarithms logb (xy)=logb x+logb y; the logarithm of a product is equal to the sum of the logarithm of the factors.        
    product rule for exponents xm⋅xn=xm+n; the product of two expressions with the same base can be simplified by adding the exponents.        
    product rule for exponents xm⋅xn=xm+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.        
    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.        
    quadratic form An equation of the form au2+bu+c=0 where a, b and c are real numbers and u represents an algebraic expression.        
    quadratic form An equation of the form au2+bu+c=0 where a, b and c are real numbers and u represents an algebraic expression.        
    quadratic formula The formula x=−b±b2−4ac2a, which gives the solutions to any quadratic equation in the standard form ax2+bx+c=0, where a, b, and c are real numbers and a≠0.        
    quadratic formula The formula x=−b±b2−4ac2a, which gives the solutions to any quadratic equation in the standard form ax2+bx+c=0, where a, b, and c are real numbers and a≠0.        
    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 logb (xy)=logb x−logb y; the logarithm of a quotient is equal to the difference of the logarithm of the numerator and the logarithm of the denominator.        
    quotient property of logarithms logb (xy)=logb x−logb y; the logarithm of a quotient is equal to the difference of the logarithm of the numerator and the logarithm of the denominator.        
    quotient rule for radicals Given real numbers An and Bn,  ABn=AnBn where B≠0.        
    quotient rule for radicals Given real numbers An and Bn,  ABn=AnBn where B≠0.        
    quotients with negative exponents x−ny−m=ymxn , given any integers m and n, where x≠0  and y≠0.        
    quotients with negative exponents x−ny−m=ymxn , given any integers m and n, where x≠0  and y≠0.        
    radical Used when referring to an expression of the form An.        
    radical Used when referring to an expression of the form An.        
    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, An.        
    radicand The expression A within a radical sign, An.        
    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)=1x.        
    reciprocal function The function defined by f(x)=1x.        
    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 a×10n, where n is an integer and 1≤a<10.        
    scientific notation Real numbers expressed the form a×10n, where n is an integer and 1≤a<10.        
    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=prt, where p represents the principal amount invested at an annual interest rate r for t years.        
    Simple interest Modeled by the formula I=prt, where p represents the principal amount invested at an annual interest rate r for t years.        
    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 A radical where the radicand does not consist of any factors that can be written as perfect powers of the index.        
    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 (x1,y1) and (x2,y2) is given by the formula m=y2−y1x2−x1.        
    slope formula The slope of the line through the points (x1,y1) and (x2,y2) is given by the formula m=y2−y1x2−x1.        
    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.        
    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.        
    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)=x.        
    square root function The function defined by f(x)=x.        
    square root function The function defined by f(x)=x.        
    square root function The function defined by f(x)=x.        
    square root property For any real number k, if x2=k, then x=±k.        
    square root property For any real number k, if x2=k, then x=±k.        
    squaring function The quadratic function defined by f(x)=x2.        
    squaring function The quadratic function defined by f(x)=x2.        
    squaring property of equality Given real numbers a and b, where a=b, then a2=b2.        
    squaring property of equality Given real numbers a and b, where a=b, then a2=b2.        
    standard form Any quadratic equation in the form ax2+bx+c=0, where a, b, and c are real numbers and a≠0.        
    standard form Any quadratic equation in the form ax2+bx+c=0, where a, b, and c are real numbers and a≠0.        
    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: (f−g)(x)=f(x)−g(x).        
    subtraction Subtract functions as indicated by the notation: (f−g)(x)=f(x)−g(x).        
    sum of squares a2+b2, where a and b represent algebraic expressions. This does not have a general factored equivalent.        
    sum of squares a2+b2, where a and b represent algebraic expressions. This does not have a general factored equivalent.        
    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 .        
    TBA Given any real number a, a+(−a)=(−a)+a=0.        
    TBA Given real numbers a, b and c, (a+b)+c=a+(b+c).        
    TBA Given real numbers a and b, a+b=b+a.        
    TBA Given any real number a, a⋅0=0⋅a=0 .        
    TBA Given any real number a, a⋅1=1⋅a=a .        
    TBA Given any real numbers a, b and c, (a⋅b)⋅c=a⋅(b⋅c).        
    TBA Given any real numbers a and b, a⋅b=b⋅a.        
    TBA Given real numbers An and Bn,  A⋅Bn=An⋅Bn.        
    TBA Given real numbers An and Bn,  ABn=AnBn.        
    TBA (xy)n=xnyn; if a product is raised to a power, then apply that power to each factor in the product.        
    TBA (xy)n=xnyn ; if a quotient is raised to a power, then apply that power to the numerator and the denominator.        
    TBA xmxn=xm−n; the quotient of two expressions with the same base can be simplified by subtracting the exponents.        
    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 .        
    TBA Given any real number a, a+(−a)=(−a)+a=0.        
    TBA Given real numbers a, b and c, (a+b)+c=a+(b+c).        
    TBA Given real numbers a and b, a+b=b+a.        
    TBA Given any real number a, a⋅0=0⋅a=0 .        
    TBA Given any real number a, a⋅1=1⋅a=a .        
    TBA Given any real numbers a, b and c, (a⋅b)⋅c=a⋅(b⋅c).        
    TBA Given any real numbers a and b, a⋅b=b⋅a.        
    TBA Given real numbers An and Bn,  A⋅Bn=An⋅Bn.        
    TBA Given real numbers An and Bn,  ABn=AnBn.        
    TBA (xy)n=xnyn; if a product is raised to a power, then apply that power to each factor in the product.        
    TBA (xy)n=xnyn ; if a quotient is raised to a power, then apply that power to the numerator and the denominator.        
    TBA xmxn=xm−n; the quotient of two expressions with the same base can be simplified by subtracting the exponents.        
    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 50 is left without meaning and is not assigned an interpretation.        
    undefined A quotient such as 50 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.        
    uniform motion The distance D after traveling at an average rate r for some time t can be calculated using the formula D=rt.        
    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.        
    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.        
    union The set formed by joining the individual solution sets indicated by the logical use of the word “or” and denoted with the symbol ∪.        
    union The set formed by joining the individual solution sets indicated by the logical use of the word “or” and denoted with the symbol ∪.        
    unit circle The circle centered at the origin with radius 1; its equation is x2+y2=1.        
    unit circle The circle centered at the origin with radius 1; its equation is x2+y2=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.        
    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.        
    variables Letters used to represent numbers.        
    variables Letters used to represent numbers.        
    vertex form A quadratic function written in the form f(x)=a(x−h)2+k.        
    vertex form A quadratic function written in the form f(x)=a(x−h)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: (h,k).        
    vertex form The equation of a parabola written in standard form is often called vertex form. In this form the vertex is apparent: (h,k).        
    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 1t1⋅t+1t2⋅t=1, where 1t1 and 1t2 are the individual work rates and t is the time it takes to complete the task working together.        
    work-rate formula 1t1⋅t+1t2⋅t=1, where 1t1 and 1t2 are the individual work rates and t is the time it takes to complete the task working together.        
    x-intercept The point (or points) where a graph intersects the x-axis, expressed as an ordered pair (x, 0).        
    x-intercept The point (or points) where a graph intersects the x-axis, expressed as an ordered pair (x, 0).        
    y-intercept The point (or points) where a graph intersects the y-axis, expressed as an ordered pair (0, y).        
    y-intercept The point (or points) where a graph intersects the y-axis, expressed as an ordered pair (0, y).        
    zero as an exponent x0=1 ; any nonzero base raised to the 0 power is defined to be 1.        
    zero as an exponent x0=1 ; 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.