I-7 INDEX in n unknowns, 874 standard form of, 239, 259 Linear equations in one variable definition of, 106 graphing calculator method for solving, 260 – 261 modeling with, 116–117 solution of, 106 solving by graphing, 260–261 Linear equations in two variables graphing calculator method for solving, 875, 877 modeling with, 259–260 point-slope form of, 253 slope-intercept form of, 254 standard form of, 239 summary of, 259 Linear functions definition of, 238 graphing, 238 point-slope form of, 253 slope-intercept form of, 254 x-intercept of graph of, 238 y-intercept of graph of, 238 Linear inequalities in one variable applications of, 170 definition of, 168 solving, 168 – 170 standard form of, 168 Linear inequalities in two variables graphs of, 939–942 standard form of, 939 Linear methods for solving trigonometric equations, 740 Linear models, 116, 245 Linear programming constraints for, 943 definition of, 942 fundamental theorem of, 943 steps to solve problems with, 942 Linear regression, 260 Linear speed applications of, 613–614 definition of, 612 formula for, 612 Linear systems, 874. See also Systems of linear equations Line segments, 526 Lissajous figure, 858 Literal equation, 109 Logarithmic differentiation, 470 Logarithmic equations definition of, 464 solving, 464 – 465, 492 – 494 steps to solve, 494 Logarithmic functions characteristics of graphs of, 467 graphs of, 465–469 modeling with, 478, 480, 495–496 standard form of, 465 Logarithms argument of, 463 base of, 463 change-of-base theorem for, 482 common, 477 definition of, 463 natural, 480 properties of, 469, 489 Inverse variation definition of, 413 as nth power, 413 Irrational numbers, 20 Is greater than, 24 Is less than, 24 J Joint variation, 413 Julia set, 824 Jump discontinuity, 391 K kth term of the binomial expansion, 1078 L Laffer curve, 400 Lambert’s law, 696 Latitude, 598 Law of cosines applications of, 789–790 applying to solve a triangle, 787 derivation and statement of, 787 – 788 Heron’s formula and, 792–794 Law of sines ambiguous case of, 776 applications of, 774–775 derivation and statement of, 773 Leading coefficient, 324 Least common denominator (LCD) explanation of, 5 finding, 5 – 6 in fractions, 75 steps to find, 75 Legs of a right triangle, 143 Leibniz notation, 481 Lemniscates, 845, 847 Leonardo of Pisa, 1042 Life table, 1109 Like radicals, 87 Like terms, 51 Limaçons, 846, 847 Limit(s) definition of, 25 of a function, 25, 227 at infinity, 389 notation, 25, 227 one-sided, 385 of the sum of the terms of an infinite geometric sequence, 1065 Line(s) definition of, 526 equation of, 253 horizontal, 239, 242, 256, 259 parallel, 256 perpendicular, 256 polar form of, 842 secant, 301 segment of, 526 slope of, 240–244 vertical, 239, 241–242, 256, 259 Linear cost function, 245 Linear equations definition of, 106, 874 Infinite geometric series, 1064–1066 Infinite sequence, 1040 Infinite series, 1043–1044 Infinite set, 15 Infinity, limits at, 389 Inflection point, 269 Initial point of a vector, 801 Initial side of an angle, 526 Inner product of vectors, 814 Input-output (function) machine, 223 Integer exponents, 40 Integers definition of, 19 relatively prime, 239 Integral(s) definite, 113, 329, 1045 of functions, 715 Intercepts of a graph, 208, 238 Interest compound, 454 simple, 109 Intermediate value theorem, 367 Intersection of sets, 18, 19, 1100 Interval(s) closed, 169 definition of, 169 disjoint, 173 notation, 169 open, 169 summary of types of, 169 Inverse additive, 26, 32 multiplicative, 26, 32, 966 Inverse cosecant function definition of, 730 graph of, 730 Inverse cosine function definition of, 728 graph of, 728–729 Inverse cotangent function definition of, 730 graph of, 730 Inverse functions definition of, 437, 725 equation of, 438–439 facts about, 442 graphs of, 441 – 442, 726 – 730 notation for, 437, 725 review of, 724–725 theorem on, 472 Inverse properties, 26, 32 Inverse secant function definition of, 730 graph of, 730 Inverse sine function definition of, 726 graph of, 726–727 Inverse tangent function definition of, 729 graph of, 729–730 Inverse trigonometric equations, 753 – 756 Inverse trigonometric functions domains and ranges of, 731 equations containing, 753–756 graphs of, 726–730 notation for, 725 summary of, 731
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