Chapter 1 Vocabulary identity - A statement that equates two equivalent expressions. verbal model- A word equation that represents a real-life problem. algebraic expression - An expression with variables. exponent - The number in a power that represents the number of times the base is used as a factor. equation - A statement in which two expressions are equal. terms - The parts of an algebraic expression that are added together. numerical expression - An expression that consists of numbers, operations, and grouping symbols. variable - A letter that is used to represent one or more numbers. value - The result when the variables in an algebraic expression are replaced by numbers and the expression is simplified. coordinate - The number that corresponds to a point on a number line. rational numbers - Numbers that can be written as the ratio of two integers. integers - The numbers..., -3, -2, -1, 0, 1, 2, 3,... graph of a real number - The point on a number line that corresponds to a number. order of operations - Set of rules that gives the order in which operations should be performed when evaluating expressions. power - An expression such as 2 5, which represents 2 2 2 2 2 = 32.
Chapter 2 Vocabulary independent variable - The input variable in an equation. range - The set of output values for the relation. relation - A mapping, or pairing, of input values with output values. step function - A piecewise function whose graph resembles a set of stair steps. linear function - A function of the form y = mx + b where m and b are constants. Its graph is a line. piecewise function - A function represented by a combination of equations, each corresponding to a part of the domain. function - A relation with exactly one output for each input. "x" intercept - The x-coordinate of the point where a line intersects the x-axis. parallel lines - Two lines in a plane that do not intersect. dependent variable - The output variable in an equation, which depends on the value of the input variable. domain - The set of input values for the relation. slope - The ratio of vertical change (the rise) to horizontal change (the run) for a nonvertical line.
Chapter 3 Vocabulary "y" intercept - If the graph of an equation intersects the y-axis at the point (0, b), then the number b. Given the equation of the graph, it is the value of y when x = 0. " z" axis - The vertical line through the origin and perpendicular to the xycoordinate plane in a three-dimensional coordinate system. three dimensional coordinate system - Is a coordinate system determined by three mutually perpendicular axes. octants - When taken pairwise, the axes of a three-dimensional coordinate system form three coordinate planes that divide space into eight parts objective function - In linear programming, the linear function that is optimized. Linear combination - A method for solving linear systems. Step 1: Multiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables. Step 2: Add the revised equations from Step 1. Combining like terms will eliminate one of the variables. Solve for the remaining variable. Step 3: Substitute the value obtained in Step 2 into either of the original equations and solve for the other variable. constraints - In linear programming, the linear inequalities that form a system. optimization - A process in which you find the maximum or minimum value of some variable quantity. system two of linear equations - Two equations of the form Ax + By = C and Dx + Ey = F where x and y are variables, A and B are not both zero, and D and E are not both zero. feasible region - In linear programming, the graph of the system of constraints. "x" intercept - The x-coordinate of the point where a line intersects the x-axis. Given an equation of the line, it is the value of x when y = 0. solution - An ordered pair (x, y) that makes the equation a true statement when the values of x and y are substituted in the equation. slope - The ratio of vertical change (the rise) to horizontal change (the run) for a nonvertical line.
Chapter 4 Vocabulary column matrix - A matrix with only 1 column. Cramer's rule - A method for solving a system of linear equations which uses determinants of matrices. solution - An ordered pair (x, 0) that satisfies each equation of the system. equal matrices - Matrices that have the same dimensions and equal entries in corresponding positions. matrix - A rectangular arrangement of numbers in rows and columns. dimensions - The number m of rows of a matrix by the number n of columns of a matrix, written m x n. constant term - A term that has no variable part. entries - The numbers in a matrix. zero matrix - A matrix whose entries are all zeros. row matrix - A matrix with only 1 row. square matrix - A matrix with the same number of rows and columns. scalar - A real number by which you multiply a matrix.
Chapter 5 Vocabulary vertex - The point of a parabola that lies on the axis of symmetry. radicand - The number or expression beneath a radical sign. trinomial - An expression with three terms. factoring - A process used to write a polynomial as a product of other polynomials having equal or lesser degree. parabola - The set of all points equidistant from a point called the focus and a line called the directrix. complex conjugates - Two complex numbers of the form a + bi and a - bi. Their product is always a real number. vertex form - The form y = a(x - h) 2 + k where the vertex of the graph us (h, k) and the axis of symmetry is x = h. complex number - A number a + bi where a and b are real numbers and i is the imaginary unit. rationalizing - The process of eliminating a radical in the denominator of a fraction by multiplying both the numerator and the denominator by an appropriate radical. monomial - An expression with one term. binomial - An expression with two terms.
Chapter 6 Vocabulary fundamental theorem of algebra - If f(x) is a polynomial of degree n where n > 0, then the equation f(x) = 0 has at least one root in the set of complex numbers. repeated solution - For the equation f(x) = 0, if and only if the factor (x - k) has degree greater than 1 when f is factored completely. end behavior - The behavior of the graph of a function as x approaches positive infinity or negative infinity. standard form - The form of a polynomial function where the terms are written in descending order of exponents from left to right. polynomial long division - A method used to divide polynomials similar to the way you divide numbers. factoring by grouping - A method used to factor some polynomials with pairs of terms that have a common monomial factor. synthetic division - is a method used to divide a polynomial by an expression of the form x - k. quadratic form - The form au 2 + bu + c where u is any expression in x. "x" intercept - The x-coordinate of the point where a line intersects the x-axis. Given an equation of the line, it is the value of x when y = 0. remainder theorem - If a polynomial f(x) is divided by x - k, then the remainder is r = f(k). power - An expression such as 2 5, which represents 2 2 2 2 2 = 32. factor theorem - A polynomial f(x) has a factor x - k if and only if f(k) = 0.
Chapter 7 Vocabulary relation - A mapping, or pairing, of input values with output values. median - The middle number when n numbers are written in order. (If n is even, it is the mean of the two middle numbers.) statistics - Numerical values used to summarize and compare sets of data. inverse functions - A relation and its inverse relation whenever both relations are functions. range - The difference between the greatest and least data values. mode - The number or numbers that occur most frequently in a set of n numbers. mean - The sum of n numbers divided by n. Also called average. exponent - The number in a power that represents the number of times the base is used as a factor. measures of dispersion - Used statistics that tell you how spread out the data are. They include the range and the standard deviation. like radicals - Two radical expressions that have the same index and the same radicand. frequency distribution - A table that shows the frequencies for the intervals into which data are grouped. square root - What r is in r 2 = s. standard deviation - is the typical difference between the mean and a data value.
Chapter 8 Vocabulary relation - A mapping, or pairing, of input values with output values. base - What b is in a function involving the expression b x where b is a positive number other than 1. natural logarithm - The logarithm with base e. exponential function - involves the expression b x where the base b is a positive number other than 1. exponential decay function - is a function of the form f(x) = ab x where a > 0 and 0 < b < 1 (decrease). exponent - The number in a power that represents the number of times the base is used as a factor. growth factor - The quantity 1 + r in the exponential growth model y = a(1 + r) t where a is the initial amount and r is the percent increase expressed as a decimal. base of power - The number in a power that is used as a factor. inverse function - A relation and its inverse relation whenever both relations are functions. decay factor - The quantity 1 - r in the exponential decay model y = a(1 - r) t where a is the initial amount and r is the percent decrease expressed as a decimal. function - A relation with exactly one output for each input. power - An expression such as 2 5, which represents 2 2 2 2 2 = 32. asymptote - A line that a graph approaches as you move away from the origin.
Chapter 9 Vocabulary joint variation - A relationship that occurs when a quantity varies directly as the product of two or more other quantities verbal model - A word equation that represents a real-life problem. "y" intercept - If the graph of an equation intersects the y-axis at the point (0, b). Given the equation of the graph, it is the value of y when x = 0. complex fraction - A fraction that contains a fraction in its numerator or denominator. asymptote - A line that a graph approaches as you move away from the origin. hyperbola - The set of all points P such that the difference of the distances from P to two fixed points, called the foci, is constant. branches - The two symmetrical parts of a hyperbola. relation - A mapping, or pairing, of input values with output values. "x" intercept - The x-coordinate of the point where a line intersects the x-axis. Given an equation of the line, it is the value of x when y = 0. direct variation - y = kx where k is a nonzero constant. cross multiplying - A method of solving a simple rational equation for which each side of the equation is a single rational expression. Equal products are formed by multiplying the numerator of each expression by the denominator of the other.
Chapter 10 Vocabulary transverse axis - The line segment joining the vertices of the hyperbola. circle - The set of all points (x, y) that are equidistant from a fixed point, called the center. hyperbola - The set of all points P such that the difference of the distances from P to two fixed points, called the foci, is constant. vertex - This point is the lowest or highest point on a parabola with a vertical axis of symmetry and the leftmost or rightmost point on a parabola with a horizontal axis of symmetry. radius - The distance r between the center of the circle and any point (x, y) on the circle. directrix - Perpendicular to the axis of symmetry. parabola - The set of all points equidistant from a point called the focus and a line called the directrix. minor axis - The line segment joining the two co-vertices of an ellipse. ellipse - The set of all points P such that the sum of the distances between P and two distinct fixed points, called foci, is a constant. conic section - A curve formed by the intersection of a plane and a doublenapped cone. co-vertices - The points of intersection of an ellipse and the line perpendicular to the major axis at the center. focus - Lies on the axis of symmetry of a parabola.
Chapter 11 Vocabulary terms - For a sequence of numbers, the numbers in the sequence. geometric series - The expression formed by adding the terms of a geometric sequence. arithmetic sequence - A sequence in which the difference between consecutive terms is constant. rational numbers - Numbers that can be written as the ratio of two integers. factorial - The expression n! and represents the product of all integers from 1 to n. range - The set of output values for the relation. domain - The set of input values for the relation. integers - The numbers..., -3, -2, -1, 0, 1, 2, 3,... geometric sequence- A sequence in which the ratio of any term to the previous term is constant. function - A relation with exactly one output for each input. finite sequence - A sequence that has a last term. sequence - A function whose domain is a set of consecutive integers. common difference - The constant difference between consecutive terms of an arithmetic sequence. finite differences - To decide whether y-values for equally-spaced x-values can be modeled by a polynomial function. series - The expression that results when the terms of a sequence are added.
Chapter 12 Vocabulary factorial - The expression n! and represents the product of all integers from 1 to n. symmetric distribution - A distribution in which the left half of the histogram representing the distribution is a mirror image of the right half. dependent events - Two events such that the occurrence of one affects the occurrence of the other. independent events - Two events such that the occurrence of one has no effect on the occurrence of the other. experimental probability - A calculation of the probability of an event based on performing an experiment, conducting a survey, or looking at the history of an event. probability - A number between 0 and 1 that indicates the likelihood an event will occur. compound event - The union or intersection of two events. combination - A selection of r objects from a group of n objects where the order is not important. standard deviation - The typical difference between the mean and a data value. permutation - An ordering of objects. fair game - A game for which the expected value is 0. geometric probability - A type of probability found by calculating a ratio of two lengths, areas, or volumes. mean - The sum of n numbers divided by n. Also called average.
Chapter 13 Vocabulary circle - The set of all points (x, y) that are equidistant from a fixed point, called the center. parameter - A variable, usually denoted t, upon which two other variables depend. parametric equations - Are equations that express two variables in terms of a third variable, called the parameter. radius - The distance r between the center of the circle and any point (x, y) on the circle. sector - A region of a circle that is bounded by two radii and an arc of the circle. co-terminal angles - Two angles in standard position with terminal sides that coincide. terminal side - The rotating ray of an angle. central angle - An angle formed by two radii of a circle. angle of depression - The angle from a horizontal line through an object A to a line connecting object A and a lower object B. radian measure - In a circle with radius r and center at the origin, The measure of an angle in standard position whose terminal side intercepts an arc of length r. domain - The set of input values for the relation.
Chapter 14 Vocabulary local minimum - The y-coordinate of a turning point of the graph of a function if the point is lower than all nearby points. frequency - The reciprocal of the period. domain - The set of input values for the relation. relation - A mapping, or pairing, of input values with output values. identity - A statement that equates two equivalent expressions. period - The horizontal length of each cycle of a periodic function. "y" intercept - If the graph of an equation intersects the y-axis at the point (0, b). Given the equation of the graph, it is the value of y when x = 0. local maximum - The y-coordinate of a turning point of the graph of a function if the point is higher than all nearby points. quadratic form - The form au 2 + bu + c where u is any expression in x. range - The set of output values for the relation. function - A relation with exactly one output for each input. "x" intercept - The x-coordinate of the point where a line intersects the x-axis. Given an equation of the line, it is the value of x when y = 0. asymptote - A line that a graph approaches as you move away from the origin. cycle - The shortest repeating portion of a periodic function.