I-5 INDEX Fundamental principle of fractions, 72 Fundamental rectangle of a hyperbola, 1016 Fundamental theorem of algebra, 350 Fundamental theorem of linear programming, 943 Future value, 109, 455, 1066–1067 ƒ1x2 notation, 227 G Galilei, Galileo, 144 Gauss, Carl Friedrich, 350 Gaussian elimination method for solving linear systems, 898–899 Gauss-Jordan method for solving linear systems, 893 General form of the equation of a circle, 214 – 215 Generalized principle of mathematical induction, 1083 – 1084 General term of a sequence, 1040 Geometric interpretation of circles, 992 Geometric progression, 1061 Geometric sequence common ratio of, 1061 definition of, 1061 infinite, 1066 nth term of, 1061 sum of infinitely many terms of, 1066 sum of terms of, 1063–1064 Geometric series definition of, 1063 infinite, 1064 – 1066 Geometry formulas, 1129 Geometry problems, 113, 142 Grade, 240, 400 Grade resistance, 558 Graph(s) of a circle, 214 of complex numbers, 821 compressed, 623 connecting with equations, 627, 650, 658 of cosecant function, 655 of cosine function, 622 of cotangent function, 646 of equations, 208 of exponential functions, 450–451 of a horizontal line, 239 horizontal translation of, 287, 360 of inequalities, 941 intercepts of, 208, 238 of inverse cosecant function, 730 of inverse cosine function, 728–729 of inverse cotangent function, 730 of inverse functions, 441–442, 726 – 730 of inverse secant function, 730 of inverse sine function, 726–727 of inverse tangent function, 729–730 of linear inequalities in two variables, 939 – 942 of logarithmic functions, 465–469 of a parabola, 269, 993 parametric, 852 constant, 230, 239 continuity of, 267–268 continuous, 267–268, 1040 cosecant. See Cosecant function cosine. See Cosine function cost, 245 cotangent. See Cotangent function cube root, 270 cubing, 269 decreasing, 230 definition of, 221 derivative of, 242, 301, 305, 348 discontinuity of, 268, 381, 391 domain of, 226, 297 even, 285, 622, 682 exponential. See Exponential functions exponential decay, 501, 503–504 exponential growth, 501–503 greatest integer, 272 identity, 268 increasing, 230 input-output machine illustration, 223 integrals of, 715 inverse, 724 – 725 inverse cosecant, 730 inverse cosine, 728–729 inverse cotangent, 730 inverse secant, 730 inverse sine, 725–727 inverse tangent, 729–730 limit of, 25, 227 linear. See Linear functions linear cost, 245 logarithmic. See Logarithmic functions logistic, 512 notation, 227, 437 objective, 943 odd, 285, 621, 682 one-to-one, 434–436, 724 operations on, 297 periodic, 620 piecewise-defined, 271 – 272 polynomial. See Polynomial functions profit, 245 quadratic. See Quadratic functions range of, 226 rational. See Rational functions reciprocal, 381 – 382 revenue, 245 secant. See Secant function sine. See Sine function sinusoidal, 638 square root, 270 squaring, 269 step, 273 tangent. See Tangent function tests for one-to-one, 436 trigonometric. See Trigonometric function(s) vertical line test for, 225 Fundamental frequency, 747 Fundamental identities, 682–683 Fundamental principle of counting, 1088 greatest common factor, 61 by grouping, 62–63 perfect square trinomial, 64–65 polynomials, 61 to solve quadratic equations, 131 – 132 substitution method for, 67 sum of cubes, 65, 66 trinomials, 63 – 65 Factor theorem, 347 Fahrenheit-Celsius relationship, 112, 265 Fan Cost Index (FCI), 889 Fibonacci, 1042 Fibonacci sequence, 1039, 1042 Finite sequence, 1040 Finite series, 1043–1044 Finite set, 15 First-degree equations definition of, 107, 874 in n unknowns, 874 Fixed cost, 245 Focus (Foci) of an ellipse, 1001 of a hyperbola, 1014 of a parabola, 994 FOIL method, 53 Four-leaved rose, 844 Fractals, 824 Fraction(s) addition of, 5–6 complex, 28, 77–78 decimal form of, 20 denominator of, 2 division of, 4–5 equivalents, 10 explanation of, 2 fundamental principle of, 72 improper, 2 least common denominator of, 5 – 6, 75 lowest terms of, 2 mixed numbers, 3 multiplication of, 3–4 numerator of, 2 operations on, 3–6 partial, 920 – 925 proper, 2 reciprocals of, 4 simplifying the, 2 subtraction of, 5–6 unit, 614 writing as decimals, 9 writing as percents, 11 writing decimals as, 7 writing percents as, 11 Fraction bar, 2, 29 Frequency definition of, 662 fundamental, 747 Frustum of a pyramid, formula for volume of, 60 Function(s) absolute value, 270–271 alternative definition of, 227 argument of, 633, 685 circular. See Circular function(s) composite, 302, 305 composition of, 302
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