# Glossary

- Page ID
- 51369

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

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 |
---|---|---|---|---|---|

(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 |
---|---|---|---|---|---|

compound inequality | A compound inequality is made up of two inequalities connected by the word “and” or the word “or.” | ||||

conditional equation | An equation that is true for one or more values of the variable and false for all other values of the variable is a conditional equation. | ||||

contradiction | An equation that is false for all values of the variable is called a contradiction. A contradiction has no solution. | ||||

identity | An equation that is true for any value of the variable is called an Identity. The solution of an identity is all real numbers. | ||||

linear equation | A linear equation is an equation in one variable that can be written, where \(a\) and \(b\) are real numbers and \(a≠0\), as \(ax+b=0\). | ||||

solution of an equation | A solution of an equation is a value of a variable that makes a true statement when substituted into the equation. | ||||

boundary line | The line with equation \(Ax+By=C\) is the boundary line that separates the region where \(Ax+By>C\) from the region where \(Ax+By<C\). | ||||

domain of a relation | The domain of a relation is all the \(x\)-values in the ordered pairs of the relation. | ||||

function | A function is a relation that assigns to each element in its domain exactly one element in the range. | ||||

horizontal line | A horizontal line is the graph of an equation of the form \(y=b\). The line passes through the y-axis at \((0,b)\). | ||||

intercepts of a line | The points where a line crosses the \(x\)-axis and the \(y\)-axis are called the intercepts of the line. | ||||

linear equation | An equation of the form \(Ax+By=C\), where \(A\) and \(B\) are not both zero, is called a linear equation in two variables. | ||||

linear inequality | A linear inequality is an inequality that can be written in one of the following forms: \(Ax+By>C\), \(Ax+By≥C\), \(Ax+By<C\), or \(Ax+By≤C\), where \(A\) and \(B\) are not both zero. | ||||

mapping | A mapping is sometimes used to show a relation. The arrows show the pairing of the elements of the domain with the elements of the range. | ||||

ordered pair | An ordered pair, \((x,y)\) gives the coordinates of a point in a rectangular coordinate system. The first number is the \(x\)-coordinate. The second number is the \(y\)-coordinate. | ||||

origin | The point \((0,0)\) is called the origin. It is the point where the \(x\)-axis and \(y\)-axis intersect. | ||||

parallel lines | Parallel lines are lines in the same plane that do not intersect. | ||||

perpendicular lines | Perpendicular lines are lines in the same plane that form a right angle. | ||||

point-slope form | The point-slope form of an equation of a line with slope \(m\) and containing the point \((x_1,y_1)\) is \(y−y_1=m(x−x_1)\). | ||||

range of a relation | The range of a relation is all the \(y\)-values in the ordered pairs of the relation. | ||||

relation | A relation is any set of ordered pairs, \((x,y)\). All the \(x\)-values in the ordered pairs together make up the domain. All the \(y\)-values in the ordered pairs together make up the range. | ||||

solution of a linear equation in two variables | An ordered pair \((x,y)\) is a solution of the linear equation \(Ax+By=C\), if the equation is a true statement when the \(x\)- and \(y\)-values of the ordered pair are substituted into the equation. | ||||

solution to a linear inequality | An ordered pair \((x,y)\) is a solution to a linear inequality if the inequality is true when we substitute the values of \(x\) and \(y\). | ||||

standard form of a linear equation | A linear equation is in standard form when it is written \(Ax+By=C\). | ||||

vertical line | A vertical line is the graph of an equation of the form \(x=a\). The line passes through the \(x\)-axis at \((𝑎,0)\). | ||||

break-even point | The point at which the revenue equals the costs is the break-even point; \(C(x)=R(x)\). | ||||

coincident lines | Coincident lines have the same slope and same \(y\)-intercept. | ||||

complementary angles | Two angles are complementary if the sum of the measures of their angles is \(90\) degrees. | ||||

consistent and inconsistent systems | Consistent system of equations is a system of equations with at least one solution; inconsistent system of equations is a system of equations with no solution. | ||||

cost function | The cost function is the cost to manufacture each unit times \(x\), the number of units manufactured, plus the fixed costs; \(C(x) = (\text{cost per unit})x+ \text{fixed costs}\). | ||||

determinant | Each square matrix has a real number associated with it called its determinant. | ||||

matrix | A matrix is a rectangular array of numbers arranged in rows and columns. | ||||

minor of an entry in a \(3×3\) determinant | The minor of an entry in a \(3×3\) determinant is the \(2×2\) determinant found by eliminating the row and column in the \(3×3\) determinant that contains the entry. | ||||

revenue | The revenue is the selling price of each unit times \(x\), the number of units sold; \(R(x) = (\text{selling price per unit})x\). | ||||

row-echelon form | A matrix is in row-echelon form when to the left of the vertical line, each entry on the diagonal is a \(1\) and all entries below the diagonal are zeros. | ||||

solutions of a system of equations | Solutions of a system of equations are the values of the variables that make all the equations true; solution is represented by an ordered pair \((x,y)\). | ||||

solutions of a system of linear equations with three variables | The solutions of a system of equations are the values of the variables that make all the equations true; a solution is represented by an ordered triple \((x,y,z)\). | ||||

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

supplementary angles | Two angles are supplementary if the sum of the measures of their angles is \(180\) degrees. | ||||

system of linear equations | When two or more linear equations are grouped together, they form a system of linear equations. | ||||

system of linear inequalities | Two or more linear inequalities grouped together form a system of linear inequalities. | ||||

binomial | A binomial is a polynomial with exactly two terms. | ||||

conjugate pair | A conjugate pair is two binomials of the form \((a−b), (a+b)\). The pair of binomials each have the same first term and the same last term, but one binomial is a sum and the other is a difference. | ||||

degree of a constant | The degree of any constant is \(0\). | ||||

degree of a polynomial | The degree of a polynomial is the highest degree of all its terms. | ||||

degree of a term | The degree of a term is the sum of the exponents of its variables. | ||||

monomial | A monomial is an algebraic expression with one term. A monomial in one variable is a term of the form \(ax^m\), where \(a\) is a constant and \(m\) is a whole number. | ||||

polynomial | A monomial or two or more monomials combined by addition or subtraction is a polynomial. | ||||

polynomial function | A polynomial function is a function whose range values are defined by a polynomial. | ||||

Power Property | According to the Power Property, \(a\) to the \(m\) to the \(n\) equals \(a\) to the \(m\) times \(n\). | ||||

Product Property | According to the Product Property, \(a\) to the \(m\) times \(a\) to the \(n\) equals \(a\) to the \(m\) plus \(n\). | ||||

Product to a Power | According to the Product to a Power Property, \(a\) times \(b\) in parentheses to the \(m\) equals \(a\) to the \(m\) times \(b\) to the \(m\). | ||||

Properties of Negative Exponents | According to the Properties of Negative Exponents, \(a\) to the negative \(n\) equals \(1\) divided by \(a\) to the \(n\) and \(1\) divided by \(a\) to the negative \(n\) equals \(a\) to the \(n\). | ||||

Quotient Property | According to the Quotient Property, \(a\) to the \(m\) divided by \(a\) to the \(n\) equals \(a\) to the \(m\) minus \(n\) as long as \(a\) is not zero. | ||||

Quotient to a Negative Exponent | Raising a quotient to a negative exponent occurs when \(a\) divided by \(b\) in parentheses to the power of negative \(n\) equals \(b\) divided by \(a\) in parentheses to the power of \(n\). | ||||

Quotient to a Power Property | According to the Quotient to a Power Property, \(a\) divided by \(b\) in parentheses to the power of \(m\) is equal to \(a\) to the \(m\) divided by \(b\) to the \(m\) as long as \(b\) is not zero. | ||||

standard form of a polynomial | A polynomial is in standard form when the terms of a polynomial are written in descending order of degrees. | ||||

trinomial | A trinomial is a polynomial with exactly three terms. | ||||

Zero Exponent Property | According to the Zero Exponent Property, \(a\) to the zero is \(1\) as long as \(a\) is not zero. | ||||

degree of the polynomial equation | The degree of the polynomial equation is the degree of the polynomial. | ||||

factoring | Splitting a product into factors is called factoring. | ||||

greatest common factor | The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions. | ||||

polynomial equation | A polynomial equation is an equation that contains a polynomial expression. | ||||

quadratic equation | Polynomial equations of degree two are called quadratic equations. | ||||

zero of the function | A value of \(x\) where the function is \(0\), is called a zero of the function. | ||||

Zero Product Property | The Zero Product Property says that if the product of two quantities is zero, then at least one of the quantities is zero. | ||||

complex rational expression | A complex rational expression is a rational expression in which the numerator and/or denominator contains a rational expression. | ||||

critical point of a rational inequality | The critical point of a rational inequality is a number which makes the rational expression zero or undefined. | ||||

extraneous solution to a rational equation | An extraneous solution to a rational equation is an algebraic solution that would cause any of the expressions in the original equation to be undefined. | ||||

proportion | When two rational expressions are equal, the equation relating them is called a proportion. | ||||

rational equation | A rational equation is an equation that contains a rational expression. | ||||

rational expression | A rational expression is an expression of the form \(\frac{p}{q}\), where \(p\) and \(q\) are polynomials and \(q≠0\). | ||||

rational function | A rational function is a function of the form \(R(x)=\frac{p(x)}{q(x)}\) where \(p(x)\) and \(q(x)\) are polynomial functions and \(q(x)\) is not zero. | ||||

rational inequality | A rational inequality is an inequality that contains a rational expression. | ||||

similar figures | Two figures are similar if the measures of their corresponding angles are equal and their corresponding sides have the same ratio. | ||||

simplified rational expression | A simplified rational expression has no common factors, other than \(1\), in its numerator and denominator. | ||||

complex conjugate pair | A complex conjugate pair is of the form \(a+bi, a-bi\) | ||||

complex number | A complex number is of the form \(a+bi\), where \(a\) and \(b\) are real numbers. We call \(a\) the real part and \(b\) the imaginary part. | ||||

complex number system | The complex number system is made up of both the real numbers and the imaginary numbers. | ||||

imaginary unit | The imaginary unit \(i\) is the number whose square is \(–1\). \(i^2 = -1\) or \(i=\sqrt{-1}\). | ||||

like radicals | Like radicals are radical expressions with the same index and the same radicand. | ||||

radical equation | An equation in which a variable is in the radicand of a radical expression is called a radical equation. | ||||

radical function | A radical function is a function that is defined by a radical expression. | ||||

rationalizing the denominator | Rationalizing the denominator is the process of converting a fraction with a radical in the denominator to an equivalent fraction whose denominator is an integer. | ||||

square of a number | If \(n^2=m\), then \(m\) is the square of \(n\). | ||||

square root of a number | If \(n^2=m\), then \(n\) is a square root of \(m\). | ||||

standard form | A complex number is in standard form when written as \(a+bi\), where \(a\), \(b\) are real numbers. | ||||

discriminant | In the Quadratic Formula, \(x=\frac{-b±\sqrt{b^2-4ac}}{2a}\), the quantity \(b^2-4ac\) is called the discriminant. | ||||

quadratic function | A quadratic function, where \(a\), \(b\), and \(c\) are real numbers and \(a≠0\), is a function of the form \(f(x)=ax^2+bx+c\). | ||||

quadratic inequality | A quadratic inequality is an inequality that contains a quadratic expression. | ||||

asymptote | A line which a graph of a function approaches closely but never touches. | ||||

common logarithmic function | The function \(f(x)=\log{x}\) is the common logarithmic function with base10, where \(x>0\). \[y=\log{x} \text{ is equivalent to } x=10^y\] | ||||

exponential function | An exponential function, where \(a>0\) and \(a≠1\), is a function of the form \(f(x)=a^x\). | ||||

logarithmic function | The function \(f(x)=\log_a{x}\) is the logarithmic function with base \(a\), where \(a>0\), \(x>0\), and \(a≠1\). \[y=\log_a{x} \text{ is equivalent to } x=a^y\] | ||||

natural base | The number \(e\) is defined as the value of \((1+\frac{1}{n})^n\), as \(n\) gets larger and larger. We say, as \(n\) increases without bound, \(e≈2.718281827...\) | ||||

natural exponential function | The natural exponential function is an exponential function whose base is \(e\): \(f(x)=e^x\). The domain is \((−∞,∞)\) and the range is \((0,∞)\). | ||||

natural logarithmic function | The function \(f(x)=\ln(x)\) is the natural logarithmic function with base \(e\), where \(x>0\). \[y=\ln{x} \text{ is equivalent to } x=e^y\] | ||||

one-to-one function | A function is one-to-one if each value in the range has exactly one element in the domain. For each ordered pair in the function, each \(y\)-value is matched with only one \(x\)-value. | ||||

circle | A circle is all points in a plane that are a fixed distance from a fixed point in the plane. | ||||

ellipse | An ellipse is all points in a plane where the sum of the distances from two fixed points is constant. | ||||

hyperbola | A hyperbola is defined as all points in a plane where the difference of their distances from two fixed points is constant. | ||||

parabola | A parabola is all points in a plane that are the same distance from a fixed point and a fixed line. | ||||

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

annuity | An annuity is an investment that is a sequence of equal periodic deposits. | ||||

arithmetic sequence | An arithmetic sequence is a sequence where the difference between consecutive terms is constant. | ||||

common difference | The difference between consecutive terms in an arithmetic sequence, \(a_n−a_{n−1}\), is \(d\), the common difference, for \(n\) greater than or equal to two. | ||||

common ratio | The ratio between consecutive terms in a geometric sequence, \(\frac{a_n}{a_{n−1}}\), is \(r\), the common ratio, where \(n\) is greater than or equal to two. | ||||

finite sequence | A sequence with a domain that is limited to a finite number of counting numbers. | ||||

general term of a sequence | The general term of the sequence is the formula for writing the \(n\)th term of the sequence. The \(n\)th term of the sequence, \(a_n\), is the term in the \(n\)th position where \(n\) is a value in the domain. | ||||

geometric sequence | A geometric sequence is a sequence where the ratio between consecutive terms is always the same | ||||

infinite geometric series | An infinite geometric series is an infinite sum infinite geometric sequence. | ||||

infinite sequence | A sequence whose domain is all counting numbers and there is an infinite number of counting numbers. | ||||

partial sum | When we add a finite number of terms of a sequence, we call the sum a partial sum. | ||||

sequence | A sequence is a function whose domain is the counting numbers. |