I-10 INDEX rationalizing denominator containing, 89 – 90 rationalizing numerator containing, 90 simplifying, 86 – 87 steps to simplify, 86 subtraction of, 87–88 summary of rules for, 85 symbol for, 82 unlike, 87 Radical equations power property and, 158 solving, 158 – 160 steps to solve, 158 Radical notation, 82–86 Radical symbol, 82 Radicand, 82 Radius of a circle, 213 Range(s) of a function, 226 of inverse circular functions, 731 of a relation, 223 of trigonometric functions, 542 Rate of change, average, 243–244 Rational equations, 154–156 Rational exponents converting from radicals to, 84 converting to radicals from, 83 definition of, 45 equations with, 160–161 factoring expressions with, 67–68 Rational expressions addition of, 75–77 common factors of, 72–73 decomposition of, 920 definition of, 72 division of, 74–75 domain of, 72 least common denominator of, 75 lowest terms of, 72–73 multiplication of, 74–75 operations on, 74–77 simplifying with negative exponents, 78 – 79 subtraction of, 75–77 Rational functions definition of, 380 features of, 384 graphing by calculator, 383–384, 392 graph of, 382–384 modeling with, 392 steps to graph, 387 Rational inequalities definition of, 174 solving, 174 – 176 steps to solve, 174, 406 Rationalizing denominators, 89 – 90 Rationalizing numerators, 90 Rational numbers, 20 Rational zeros theorem, 348 Ray definition of, 526 endpoint of, 526 r cis u, 822 Real axis, 821 Pythagorean identities, 543–544, 683 Pythagorean theorem, 143 Q Quadrantal angles, 529 Quadrants of a coordinate system, 202 Quadratic equations in one variable applications of, 142 completing the square to solve, 133 discriminant of, 137–138 factoring to solve, 131 modeling with, 145 quadratic formula for solving, 134 – 136 square root method for solving, 132 standard form of, 131 types of solutions for, 138 Quadratic formula discriminant of, 137–138 standard form of, 135 Quadratic functions definition of, 324 graph of, 324–326 maximum of, 328 minimum of, 327 steps to graph, 329 Quadratic inequalities definition of, 171 solving, 171 – 174 steps to solve, 171 Quadratic models, 145, 330 Quadratic regression, 332 Queuing theory, 399 Quotient, 26 Quotient identities, 544, 683 Quotient rule for exponents, 43, 47 Quotient theorem for complex numbers, 827 R Radian, 594 Radian/degree relationship converting measures, 594–595 table of, 596 Radian measure applications of, 598–599 converting to degree measure, 594 – 595 definition of, 594 Radiative forcing, 481 Radical(s) addition of, 87–88 conjugate of, 90 converting from rational exponents to, 83 converting to rational exponents from, 84 index of, 82, 85 like, 87 multiplication of, 88–89 negative root of, 83 notation, 82 – 86 operations with, 87–89 principal root of, 83 intermediate value theorem for, 367 leading coefficient of, 324 modeling with, 369–370 number of zeros theorem for, 350 – 351 of odd degree, 361 rational zeros theorem for, 348 roots of, 344 solutions of, 344, 365 steps to graph, 364 turning points of graph of, 362 zero, 324 zeros of, 344, 353, 361, 365 Polynomial inequalities, 402–405 Polynomial interpolation, 976 Polynomial models, 369–370 Population growth, 1042 Position vector, 811 Positive angle, 526 Positive slope, 243 Power property of equations, 158 Power rule(s) for derivatives, 84 for exponents, 40–42, 47 Power series, 182 Powers of complex numbers, 832 Powers of i, 128 – 129 Powers of ten division by, 8–9 explanation of, 7 multiplication by, 8–9 Present value, 455 Prime polynomial, 61 Principal root of a radical, 83 Principle of mathematical induction, 1080 – 1081 Probability of an event, 1099 basics of, 1099–1106 binomial, 1105 of compound events, 1103 definition of, 1099 properties of, 1105 of union of events, 1102–1103 Product definition of, 26 of the sum and difference of two terms, 54 Product rule for exponents, 40, 47 Product theorem for complex numbers, 826 Product-to-sum identities, 715–716 Profit function, 245 Progression arithmetic, 1051 geometric, 1061 Proper fractions, 2 Properties of parallelograms, 802 Proportional directly, 411 as nth power, 412–413 Proposed solutions, 154 Ptolemy, 565, 786 Pure imaginary number, 124 Pyramid frustum of, 60 volume of a frustum of, 60 Polynomial functions (continued)
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