Subject Index I5 equations of, of even and odd functions, 88–89 even, 87–89 exponential, graphs/graphing of, 298–302 graphs/graphing of compressions and stretches for, 115–117 determining where function is increasing, decreasing, or constant from, 89–90 of exponential functions, 298–302 of functions in library of functions, 100–105 of inverse functions, obtaining from graph of a one-to-one function, 285 of a linear function, 139 locating absolute maximum and minimum using, 91–93 locating local maxima and minima using, 90–91, 93 obtaining information from or about, 78–81 of odd and even functions, 87–89 of rational functions, 238, 239, 247–258 reflections about the x-axis or y-axis for, 117–118 of secant function, 447–448 of sine function, 427–429 of sinusoidal functions, 432–435, 451–455, 589 of sum of two functions, 588–589 of tangent function, 443–444, 445–447 tangent line to, equation of, 961–962 transformations for, 112–126 vertical and horizontal shifts for, 112–114 greatest integer, 104 identity, 102–103 limits of, 946 implicit form of, 68 increasing, 90–91, 93 linear, 142 initial value of, 143 inverse, 283–289 defined by a mapping or a set of ordered pairs, 283–284 definition of, 283 of a domain-restricted function, 289 of a function defined by an equation, 286–289 graph of, obtaining from graph of a one-to-one function, 285 of a logarithmic function, 316–319 trigonometric. See Inverse trigonometric functions verifying, 286–287 library of, 100–105 linear definition of, 139 graphing, 139 identifying, 297–298 identifying using average rate of change, 139–142 increasing, decreasing, or constant, 142 modeling using, 143–145 local maxima and minima of, 90–91, 93 natural logarithm, 316 nonlinear, 139 objective, 841 odd, 87–89 one-sided limits of, 953–955 one-to-one, 281–283 definition of, 281 graph of, obtaining inverse function from, 285 horizontal-line test for, 282–283 periodic, 415 piecewise-defined, 105–107 continuous at a number, determining, 957 polynomial. See Polynomial functions power, 191–193 AC generators and, 440 definition of, 191 of even degree, 192–193 of odd degree, 193 product, 71, 72 quotient, 72, 73 for an arithmetic sequence, 871 sequences defined by, terms of, 858–859 solving annuity and amortization problems using, 862–864 rotation, 722 simple interest, 345, A67 solving annuity problems using, 880–881 for special products, A24–A25 Sum and Difference, 511–524 for cosine function, 511–512 establishing identities using, 516–517 finding exact values using, 512–515 involving inverse trigonometric functions, 517–518 solving trigonometric equations linear in sine and cosine and, 518–520 Sum-to-Product, 536–537 uniform motion, A70 Fraction(s) continued, A43 partial, 813. See also Partial fraction decomposition proper and improper, 813 writing expressions containing fractional exponents as radicals and, A91 Fractional exponents, expressions containing, writing as radicals, A91 Frequency AC generators and, 440 of objects in simple harmonic motion, 585 Friction, coefficient of, 649 Frobenius, Georg, 808 Function(s), 61–77 absolute maximum and minimum of, 91–93 absolute value, 101–102, 104 computing, A5 definition of, A5 of z, 628 in applications, domain of, 71 area under graph of, approximating, 969–972 argument of, 66 average rate of change of, 93–96 building and analyzing, 126–131 calculus and critical numbers for, 869 increasing, decreasing, or constant, 362 local maximum and local minimum in, 93 circular, 398. See also Trigonometric functions codomain of, 63 composite, 273–280 in calculus, 277 components of, 277 definition of, 273 equal, 276–277 evaluating, 274 forming, 273–277 involving inverse trigonometric functions, exact value of, 489–490 constant, 90–91, 102 linear, 142 continuous, 104 determining, 955–958 continuous at a number, determining, 955–958 cube root, 101, 103 decreasing, 90–91, 93 linear, 142 defined by an equation domain of, 69–71 inverse functions of, 286–289 definition of, 63 derivative of, 962–963 difference, 71, 72 difference quotient of, 68–69 differentiable, 963 discontinuous at a number, 956 domain of, 63, 69–71 domain-restricted, inverse of, 289 equations as, 65 Exponential statements, changing to logarithmic statements, 313–314 Extended Principle of Mathematical induction, 897 Extraneous solutions, A90 Extreme Value Theorem, 92–93 Factor(s), A27 linear, 814 nonrepeated, decomposition and, 814–815 repeated, decomposition and, 815–817 monomial, identifying, A28 quadratic, irreducible nonrepeated, decomposition and, 817–818 nrepeated, decomposition and, 818–819 verifying using synthetic division, A34 Factorial symbol, 858 Factoring of expressions containing rational exponents, A91, A92 of polynomials, A27–A28 completely, A27 over the integers, A27 solving a quadratic equation by, A48–A49 solving equations by, A54–A55 Factor Theorem, 216–217 Family of lines, 47 Feasible points, 841 Fermat, Pierre de, 931 Ferrari, Lodovico, 226 Ferris, George W., 54 Fibonacci, 883 Fibonacci numbers, 859–860 Fibonacci sequence, 859–860 Financial models, 345–354 effective rates of return and, 348–349 future value of a lump sum and, 345–348 present value of a lump sum and, 349–350 rate of interest or time required to double a lump sum, 350–351 Finck, Thomas, 392, 407 Finite sets, 911n First-degree equation(s), A46 First differences, 450 Fixed costs, 46 Focus/foci of a conic, 729 of an ellipse, 692 of a hyperbola, 705 of a parabola, 682 FOIL, A24 Force, resultant, 644 Force diagrams, 645 Formulas amortization, 864 annuity, 863 for an arithmetic sequence, 870–871 change-of-base, 332 compound interest, 346 counting, 912 Distance, 13–16 distance between two points in space and, 660–661 proof of, 14–15 Double-angle establishing identities using, 525–528 finding exact values using, 525 Euler’s, 629 for a geometric sequence, 877 geometry, A15–A16 Half-angle, finding exact values using, 528–530 Heron’s, historical feature on, 579 midpoint, 16 present value, 350 Product-to-Sum, 535–536 quadratic, A64 discriminant of, A52 solving quadratic equations using, A51–A53 recursive
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