I-4 INDEX probability of, 1099 union of two, 1100, 1102–1103 Eves, Howard, 203 Exact number, 566 Expansion of binomials, 1073 by a given row or column, 909 Experiment binomial, 1105 outcomes of, 1099 Explicitly defined sequence, 1041 Exponent(s) base of, 28 definition of, 28, 447 integer, 40 negative, 42 – 43, 47, 67 – 68, 78 – 79 notation for, 29, 46 properties of, 447–448 rational, 45 – 48, 67 – 68, 160 – 161 rules for, 40 – 45, 47 – 48 zero, 42 Exponential decay function definition of, 501 modeling with, 503–504 Exponential equations applications of, 495 definition of, 452 solving, 452, 489–491 steps to solve, 494 Exponential expressions definition of, 28 evaluating, 29 Exponential functions characteristics of graphs of, 451 evaluating, 449 graph of, 450–451 modeling with, 457 standard form of, 449 Exponential growth function definition of, 501 modeling with, 501–503 Expressions algebraic, 28 classifying as polynomials, 52 exponential, 28 – 29 factoring with negative or rational exponents, 67 – 68 rational. See Rational expressions roots of, 29 F Factor(s) common, 2 greatest common, 2 of a number, 28 of a polynomial function, 365 Factored form of a polynomial, 61 Factorial notation, 1074, 1089 Factoring binomials, 65 – 66 definition of, 61 difference of cubes, 65, 66 difference of squares, 65–66 expressions with negative or rational exponents, 67 – 68 connecting graphs with, 627, 650, 658 contradiction, 108, 109 cubic, 136 definition of, 106 dependent, 874 differential, 501 of an ellipse, 1003 equivalent, 106 exponential. See Exponential equations first-degree, 107, 874 graphing, 208 – 209 graph of, 208 of a horizontal line, 256 of a hyperbola, 1017 identity, 108, 109 independent, 874 of an inverse function, 438–439 of a line, 253, 254 linear. See Linear equations literal, 109 logarithmic. See Logarithmic equations nonlinear systems of. See Nonlinear systems of equations of a parabola, 992 parametric, 568, 633, 852 polar, 842 – 846 power property of, 158 quadratic in form, 161–163 quadratic in one variable. See Quadratic equations in one variable radical, 158 – 160 rational, 154 – 156 with rational exponents, 160–161 rectangular, 842, 846 roots of, 106 rotation, 1125 second-degree, 131 solution set of, 106 solutions of, 106 steps to graph, 208 trigonometric. See Trigonometric equations types of, 108, 109 of a vertical line, 256 Equilibrant vector, 803 Equilibrium demand, 891 Equilibrium price, 891 Equilibrium supply, 891 Equivalent equations, 106 Equivalent systems of linear equations, 875 Even-degree polynomial functions, 361, 363 Even function, 285, 622, 682 Even-odd identities, 682, 683 Event(s) certain, 1100 complement of, 1100 compound, 1102 – 1103 definition of, 1099 impossible, 1100 independent, 1088 mutually exclusive, 1103 odds in favor of, 1101–1102 Double-angle identities definition of, 711–712 simplifying expressions using, 714 Double solution, 132 Doubling time, 501 E e continuous compounding and, 456 eccentricity of, 850 value of, 456 Eccentricity of constant e, 850 definition of, 1007 of a circle, 1008, 1020 of a conic, 1007 of an ellipse, 1008–1009, 1020 of a hyperbola, 1019–1020 of a parabola, 1007, 1020 Element cofactor of, 909 of a matrix, 892 minor of, 908 of a set, 15 Elevation, angle of, 569, 573 Elimination method definition of, 875 for solving linear systems, 875, 880 for solving nonlinear systems, 929 Ellipse(s) applications of, 1009–1010 center of, 1002 definition of, 1001 eccentricity of, 1008–1009, 1020 equations of, 853, 1003 foci of, 1001 geometric definition of, 1002 geometric interpretation of, 992 major axis of, 1002 minor axis of, 1002 reflective property of, 1010 translations of, 1005–1006 vertices of, 1002 Empty set definition of, 16, 108 symbol for, 16, 108 End behavior of graphs of polynomial functions, 362, 363 Endpoint of a ray, 526 Envelopes, 664, 1000 Epitrochoids, 854 Equality addition property of, 106 multiplication property of, 106 Equal matrices, 951 Equal sets, 17 Equation(s) absolute value, 181–182 Cartesian, 842 of a circle, 213–216 for compound interest, 454 conditional, 108, 109 conditional trigonometric. See Conditional trigonometric equations of conic sections, 1025, 1127
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