Radical(s), 61

• with different indices, 66–67

• equations involving, 133–136

• like, 65–66

• rules for, 65

Radical expressions

• adding and subtracting, 65–66

• conjugates, 67–68

• defined, 64

• rationalizing, 67

Radical sign $(\sqrt{})$, 61, 64

Radicand, 61, 64

Radioactive decay, 469–470

Radiocarbon dating, 470–471

Radius of a circle, 191

Range of a function, 221, 223

• of an exponential function, 426

• of a one-to-one function, 300–301

• of a quadratic function, 323

Range of a relation, 217

Rate of change, average, 241–244

Rate of work, 97

Rational approximations of irrational numbers, 4

Rational equations, 132–133

• with extraneous solutions, 132

Rational exponents, 68–71

• equations with, 136–137

Rational expressions, 50–60

• adding and subtracting, 53–56

• complex fractions as, 56–57

• defined, 50

• dividing, 52–53

• least common denominator for, 54–56

• multiplying, 52–53

• proper and improper, 540

• reducing to lowest terms, 51–52

Rational functions, 384–402

• graphing, 388–389, 392–398

• with graphs having a hole, 390

• translations for graphing, 388–389

• vertical and horizontal asymptotes of, 386–388, 389

Rational inequalities, test-point method for solving, 152–153

Rationalizing the denominator/numerator, 67–68

Rational numbers, 3–4

Rational power functions, 258

Rational Zeros Theorem, 365–367

Real line. See Number line

Real number(s), 2–19. See also Number line

• absolute value of, 9–10

• algebraic expressions and, 14–16

• division of, 13–14

• inequalities and, 6–7

• as integer exponents, 5–6

• irrational, 4–5

• ordered pairs of, 175

• ordering of, 6

• order of operations and, 11–12

• properties of, 12

• rational, 3–4

• sets of, 3, 4–5, 7–9

• subtraction of, 13–14

Real number line. See Number line

Real part of a complex number, 120–121

Real zeros of a polynomial function, 364–375

• bounds on, 368–369

• Descartes’s Rule of Signs and, 367–368

• finding, 369–372

• odd-degree polynomials and, 379

• Rational Zeros Theorem and, 365–367

Reciprocal(s), 13

Reciprocal functions, 258

Reciprocal square function, 258

Rectangles, area of, 220

Recursive definitions, 226

Recursive formulas, 719–721

Reduced row-echelon form, 594–595

Reflecting property

• of an ellipse, 684

• of a parabola, 670–671

Reflections of graphs, 267–269

Regression line, 207–209

Relations, 217

Relative maximum/minimum of a function, 237–239

Remainder Theorem, 357–358

Research and development, profit from, 41, 45–46

Revenue, total, calculating, 610–611

Revenue curves, graphing, 396–397

Revenue function, 227

Richter, Charles Francis, 490

Richter scale, 490–493

Right circular cones, 659

Right triangles, 178, 179

• Pythagorean Theorem and, 178, 179

Rigid transformations of functions, 263, 267

Roots. See also Solutions

• double (of multiplicity 2), 108

• of equations, 82

Roster method, 7

Row-echelon form, 594

Row equivalent matrices, 592

Russell, Bertrand, 130