I6 Subject Index using vertex, axis, and intercepts, 161–163 of rational functions, 247–258 analyzing, 247–254 constructing from its graph, 253–254 end behavior of graphs of, horizontal asymptotes and, 239 with a hole, 252–253 solving applied problems involving, 254–255 with transformations, 238 of rectangular equations, identifying and graphing polar equations by converting to, 611–612 of relations, 61 of secant function, 447–448 of sine function, 427–429 sinusoidal, 431 finding an equation for, 436 of sinusoidal functions, 451–455 graphing the sum of, 589 using key points, 432–435 smooth, 191 of sum of two functions, 588–589 of systems of inequalities, in two variables, 834–837 of systems of linear equations, 757 of tangent function, 443–444, 445–447 of trigonometric equations, solving using a graphing utility, 498 of vectors, 639 vertices of, 837 Graphing calculator(s)/utility(ies), A10 analyzing graphs of polynomial functions using, 209 approximating integrals using, 972–974 approximating intercepts using, 9–10 approximating local maxima and minima of functions using, 93 approximating the value of a trigonometric function using, 405–406 connected mode using, 104 derivatives and, 963 description of, 3 dot mode using, 104 DRAW feature of, 36 equations graphed on, 6–8 evaluating powers of 2 using, 295 eVALUEate feature of, 9 exponents on, A10 graphing a circle using, 49–51 graphing a hyperbola using, 707 graphing an ellipse using, 695 graphing a parabola using, 683, 687 graphing parametric equations using, 737–738 INTERSECT feature of, 30, 31 limits and, 943 LINE feature of, 36 line of best fit using, 152–153 locating zeros of polynomial functions using, 225 PLOT feature of, 36 polar equations and, 612–613 setting viewing window (rectangle) of, 3 solving a system of linear equations using, 757 solving equations using, 28–32 solving logarithmic and exponential equations using, 341 solving rational inequalities using, 261 solving trigonometric equations using, 496, 498 square screen on, 34–35 table creation using, 8–9 VERT feature of, 36 ZERO (or ROOT) feature of, 10, 29, 31 Grassmann, Hermann, 647 Greatest integer function, 104 Greek Method, 55 Growth, uninhibited, law of, 355–357 Growth of cells, uninhibited, 355–357 Half-angle Formulas, finding exact values using, 528–530 Half-closed intervals, A77 Half-life, 357 Half-open intervals, A77 Hamilton, William Rowan, 647 of cosecant function, 447–448 of cosine function, 429–430 of cotangent function, 445–447 distance from origin to a point on, 126–127 of an equation by plotting points, 4–6 in two variables, 4 using intercepts, 39–40 of exponential functions, 298–302 finding intercepts from, 9 of functions, 77–86 compressions and stretches for, 115–117 determining where function is increasing, decreasing, or constant from, 89–90 of functions in library of functions, 100–105 inverse, obtaining from graph of a one-to-one function, 285 linear, 139 locating absolute maximum and minimum using, 91–93 locating local maxima and minima using, 90–91, 93 logarithmic, whose base is neither 10 nor e, 332–333 logarithmic , whose base is neither 10 nor e, 332–333 logarithmic functions and their inverses, 315–319 obtaining information from or about, 78–81 of odd and even functions, 87–89 one-to-one, obtaining inverse function from, 285 of one-to-one functions, obtaining inverse function from, 285 polynomial, 184, 198–201, 206–210, 224 quadratic, 158–163 rational, 238, 239, 247–258 reflections about the x-axis or y-axis for, 117–118 secant, 447–448 sine, 427–429 sinusoidal, 431, 432–435, 436, 451–455, 589 tangent, 443–444, 445–447 tangent line to, equation of, 961–962 transformations for, 112–126 vertical and horizontal shifts for, 112–114 of hyperbolas, 706–707 of inequalities, A4–A5 investigating limits using, 943–944 of key equations, 24–26 x y2 = , 24–25 y x 1 = , 25–26 y x3 = , 24 limits and, 943–944 of a line, given a point and a slope, 35 of an object in damped motion, analyzing, 587 of parabolas, 683 of parametric equations with graphing utility, 737–738 by hand, 736 of plane curves, 736 of polar equations, 611–612 cardioids and, 616–617 of conics, 728–732 by converting to rectangular equations, 611–612 with a graphing utility, 612–613 lemniscates and, 621 limaçons with an inner loop and, 619 limaçons without an inner loop and, 618 by plotting points, 616–624 roses and, 620 sketching quickly and, 623 spirals and, 621–622 of polynomial functions analyzing, 206–210 end behavior and, 198–201 identifying graphs of polynomial functions and, 198 obtaining using bounds on zeros, 224 using transformations, 194 of quadratic functions with transformations, 158–160 range of, 63 rational. See Rational functions reciprocal, 103 relations and, 61–62 representing a function, 63–65 secant, 398 graphs/graphing of, 447–448 inverse, 487–489 sine, 398 of best fit, 458–459 graphs/graphing of, 427–429 historical feature on, 407 inverse, 472–475 name of, 407 properties of, 428 sinusoidal, 430–432 amplitude, period, and phase shift of, 452–454 amplitude and period of, 431–432 graphing the sum of, 589 graphs/graphing of, 432–435, 451–455, 589 square root, 100, 103 of a negative number, evaluating, A63 step, 104 sum, 71, 72 tangent, 398 graphs/graphing of, 443–444, 445–447 inverse, 477–479 name of, 407 properties of, 444 trigonometric. See Trigonometric functions value of, 63, 65, 66–67 Function keys, on calculators, A10 Function notation, 65 Fundamental Identities finding values of trigonometric functions using, 417–419 solving trigonometric equations using, 497–498 Fundamental period of a function, 415 Fundamental Theorem of Algebra, 230 Future value of a lump sum, 345–348 Galois, Evariste, 226 Gauss, Karl Friedrich, 230, 634 Gauss-Jordan elimination, 776 General addition principle of counting, 913 General equation of a conic, 726 General form of the equation of a circle, 51–52 of a line, 39–40 General terms of an infinite series, 890 of sequences, 856 Generators of a right circular cone, 681 Geometric mean, A86 Geometric sequences (progressions), 875–879 common ratio and, 875–876 definition of, 875–876 determining, 876 formula for, finding, 877 nth term of, 877 sum of, finding, 878–879 Geometric series, 879–881, 892–893 definition of, 892 infinite, 879 sum of, 893 Geometric vectors, 637 Geometry essentials, A14–A22 congruent and similar triangles and, A16–A19 formulas and, A15–A16 Pythagorean Theorem and its converse, A14–A15 Geometry problems, solving using algebra, 15–16 Gibbs, Josiah Willard, 647 Graph(s)/graphing, 1–59 approximating the area under, 969–972 bounded and unbounded, 837 of a circle, 49–51 complete, 4–5 continuous, 191 Function(s) (continued)
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