simplifying with negative exponents,
383–384
steps to multiply, 366
subtraction of, 371
subtraction with different denominators,
374
Rational functions, 362, 389, 410
discontinuous, 389
domains of, 362, 389
graphs of, 389–390
Rational inequality, 555
steps to solve, 555
Rational numbers, 4–5
as exponents, 435
fundamental property of, 363
Rationalizing a binomial denominator, 461
Rationalizing the denominator, 459
Rationalizing the numerator, 463
Real numbers, 4–5
additive inverse of, 6, 34
graphing sets of, 9–11
multiplicative inverse of, 18, 34
operations on, 14–20
properties of, 32–36
reciprocals of, 18
Real part of a complex number, 476
Reciprocal
of a rational expression, 367
of a real number, 18
Reciprocal function, 389, 636
graph of, 389, 636
Rectangular coordinate system, 137
plotting points in, 136
quadrants of, 137
Reduced row echelon form, 253
Regions in the real number plane, 175
Relation, 182
domain of, 184
range of, 184
Relative error, 117
Remainder theorem, 725
Richter scale, 594
Right triangle, 448
hypotenuse of, 448
legs of, 448
Rise, 148
Root functions, 429–430
Roots
calculator approximation of, 432
cube, 428
fourth, 428
negative, 428
nth, 428
of numbers, 428
positive, 428
principal, 428
simplifying, 428
square, 25, 428
Row echelon form, 248
Row operations on a matrix, 248
Rows of a matrix, 247
Rule of 78, 64
Run, 148Scale, 143
Scatter diagram, 167
Scientific notation, 271–272
application of, 273
converting from scientific notation, 272
converting to scientific notation, 271
Second-degree equations, 496
Second-degree inequalities, 664
graphs of, 664
Semiperimeter, 434
Sequence, 678
arithmetic, 684
finite, 678
general term of, 678
geometric, 691
infinite, 678
terms of, 678
Series, 680
finite, 680
infinite, 680
Set(s), 2
elements of, 2
empty, 2
finite, 2
graph of, 9–11
graph of real numbers, 9–11
infinite, 2
intersection of, 103
mapping of, 183
members of, 2
null, 2
of numbers, 5
operations on, 103, 105
solution, 48
union of, 105
Set braces, 2
Set-builder notation, 2
Set operations, 103, 105
Sigma notation, 680
Signed numbers, 6
Similar triangles, 404
Simple interest, 57, 71, 616
Simplified form of a radical, 445, 466
Slope(s)
formula for, 148
of a horizontal line, 150
of a line, 148
negative, 152
of parallel lines, 152, 165
of perpendicular lines, 153, 165
positive, 152
undefined, 150, 152
of a vertical line, 150
Slope-intercept form, 161, 166
Solution of an equation, 48
Solution set, 48, 97
of a linear system, 210Solving a literal equation, 57
Solving for a specified variable, 57, 349,
396, 523
steps to solve, 57
Speed, 82
Square(s)
of a binomial, 297
difference of, 333, 337, 340
of a number, 24
sum of, 334, 340
Square matrix, 247, 715
determinant of, 715
Square root function, 429, 636
generalized, 654
graph of, 429, 636
Square root method for solving quadratic
equations, 496
Square root notation, 428
Square root property, 496
Square roots of a number, 25, 428, 474
principal, 26, 428
simplifying, 431
symbol for, 26, 428
Square viewing window, 646
Squaring function, 289, 636
Standard form
of a complex number, 476
of a linear equation, 139, 164, 166
of a quadratic equation, 344, 496
Standard viewing window, 143
Step function, 638
Study skills
analyzing test results, 225
managing time, 147
preparing for math final exam, 482
reading math textbook, 46
reviewing a chapter, 122
tackling homework, 56
taking lecture notes, 80
taking math tests, 198
using math textbook, xviii
using study cards, 102, 111
Subscript notation, 142
Substitution method
for solving quadratic equations, 516,
518
for solving systems, 212–215, 658
Subtraction
of complex numbers, 477
of polynomial functions, 285
of polynomials, 281
of radical expressions, 453–455
of radicals, 453–455
of rational expressions, 371
of real numbers, 15–16
Sum, 14
of an infinite geometric sequence, 696
of terms of a geometric sequence,
693–694, 696
of terms of an arithmetic sequence,
687, 688