rational, 435
summary of rules for, 269
zero, 265
Expressions
algebraic, 28, 48, 278
distinguishing from equations, 68
exponential, 24
radical, 429, 453
rational, 362
Extraneous solutions, 468
Factorial notation, 702
Factoring, 320
binomials, 340
difference of cubes, 335, 337, 340
difference of squares, 333, 337, 340
by grouping, 322–323
perfect square trinomials, 334, 337
polynomials, 320, 331, 339, 341
solving quadratic equations by, 345
sum of cubes, 336–337, 340
summary of special types of, 337
trinomials, 326, 341
using FOIL, 326–329
Factors
greatest common, 320
of numbers, 24
Fahrenheit-Celsius relationship, 173–174
Farads, 432
Fibonacci, 677
Finite sequence, 678
Finite set, 2
First-degree equations, 48, 139.See also
Linear equations
graph of, 139
Foci
of an ellipse, 644
of a hyperbola, 650
FOIL method, 295, 326, 328–329, 458, 477
Formula(s), 56, 523
binomial coefficient, 702–703
for compound interest, 616
distance, 449, 452
Galileo’s, 498, 563
Heron’s, 434
midpoint, 142
of the Pythagorean theorem, 427, 448,
524
quadratic, 505–506
with rational expressions, 396
solving for a specified variable of, 57,
349, 396, 523
with square roots, 523
vertex, 542
Fractional exponents, 435
radical form of, 438
Fractions
algebraic, 362
complex, 380
equivalent forms of, 20
linear equations with, 51
linear inequalities with, 96
Froude, William, 530
Froude number, 530
Function(s), 182
absolute value, 636
coding information using, 579
composite, 286–287
composition of, 286–287
constant, 193
cube root, 430
cubing, 289
definitions of, 182, 187
division of, 305
domain of, 184
equation of the inverse of, 574
exponential, 580
greatest integer, 638
identity, 288–289
inverse of, 572
linear, 193, 289
logarithmic, 590
notation, 190
one-to-one, 572
operations on, 285, 298, 305
polynomial, 284
quadratic, 531–532
radical, 429
range of, 184
rational, 362, 389
reciprocal, 389, 636
root, 429–430
square root, 429, 636, 654
squaring, 289, 636
step, 638
vertical line test for, 185
zeros of, 349
Fundamental property of rational
numbers, 363
Fundamental rectangle of a hyperbola, 651
Future value of an ordinary annuity, 695
notation, 190Galilei, Galileo, 498
Galileo’s formula, 498, 563
General binomial expansion, 703
General term
of an arithmetic sequence, 685
of a geometric sequence, 692
of a sequence, 678
Geometric progression, 691
Geometric sequence, 691
common ratio of, 691
general term of, 692
specified term of, 693
sum of terms of, 693–696
Grade, 148
Graphing calculators.SeeCalculator
graphing
Graphing method for solving systems, 211Graphs, 3, 135
of absolute value functions, 636
of circles, 642
of cube root functions, 430
of ellipses, 645
of equations, 139
of exponential functions, 580–582
of first-degree equations, 139
of a greatest integer function, 638–639
of horizontal lines, 140
of hyperbolas, 650–651
of inequalities, 9–11
of inverses, 575–576
of linear equations, 139
of linear inequalities, 175
of linear systems, 212, 226
of logarithmic functions, 590–591
of numbers, 3
of ordered pairs of numbers, 137
of parabolas, 531, 546
of polynomial functions, 288–289
of quadratic functions, 531
of quadratic inequalities, 552
of radical expressions, 429–430
of radical functions, 429–430
of rational functions, 389–390
of a reciprocal function, 636
of second-degree inequalities, 664–665
of sets of numbers, 9–11
of square root functions, 429, 636, 653
of systems of nonlinear inequalities, 665
of three-part inequalities, 11
of vertical lines, 141
Greater than, 8–9
definition of, 8
Greatest common factor (GCF), 320
factoring out, 320
Greatest integer function, 638
graph of, 639
Grouping
factoring by, 322–323
steps to factor by, 323
Growth
applications of, 584–585
exponential, 584, 618Half-life, 618
Henrys, 432
Heron’s formula, 434
Horizontal asymptote, 389
Horizontal line, 140
equation of, 140, 163–164, 166
graph of, 140
slope of, 150
Horizontal line test for a one-to-one
function, 573
Horizontal parabola, 546
graph of, 546
Horizontal shift, 637
of a parabola, 533H
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