Absolute value, 6–7, 112, 431
definition of, 7
distance definition of, 112
Absolute value equations, 113
solution of, 113, 115, 116
steps to solve, 113
Absolute value function, 636
graph of, 636
Absolute value inequalities, 113
solution of, 113–114, 116
steps to solve, 113
Addition
associative property of, 34–35
commutative property of, 34–35
of complex numbers, 477
identity element for, 33
identity property for, 33
inverse property for, 34
of polynomial functions, 285
of polynomials, 280
of radical expressions, 453–454
of rational expressions, 371
of real numbers, 14
Addition property
of equality, 49
of inequality, 92
Additive identity, 33
Additive inverse of a real number, 6, 34
Agreement on domain, 186
Algebraic expressions, 28, 48, 278
evaluating, 28
Algebraic fraction, 362
Angles
complementary, 88
supplementary, 88, 241
vertical, 87, 241
Annuity, 695
ordinary, 695
terms of, 695
Apogee, 410
of an ellipse, 649
Applied problems, steps for solving, 69
Approximately equal symbol, 432
Area problem, 234, 525
Arithmetic mean, 681
Arithmetic progression, 684
Arithmetic sequence, 684
application of, 686
common difference of, 684
general term of, 685
specified term of, 686
sum of terms of, 687–688
Array of signs for a determinant, 717
Associative properties, 34–35
Asymptotes, 636
horizontal, 389
of a hyperbola, 650
vertical, 389
Augmented matrix, 247
reduced row echelon form of, 253
Average, 681
Average rate of change, 154
Average rate of speed, 59
Axis
of a coordinate system, 137
of a parabola, 531, 534Babbage, Charles, 601
Base
of an exponent, 24, 264
of an exponential expression, 24
Binomial coefficient formula, 702–703
Binomial expansion
general, 703
specified term of, 704
Binomial theorem, 701, 703
Binomials, 279
conjugates of, 461
factoring of, 340
multiplication of, 294, 458
raising to a power, 701
square of, 297
Boundary line, 175
Braces, 2
Break-even point, 663Calculator graphing
of a circle, 646, 648
of an ellipse, 646, 648
of a hyperbola, 652
of linear inequalities, 178
of a root function, 654
Calculator graphing method
for displaying binomial
coefficients, 703
to find inverse of a function, 576
for generating quadratic models, 536
for solving exponential equations, 619
for solving linear equations, 169
for solving linear systems, 218–219
for solving logarithmic equations, 619
for solving nonlinear systems, 661
for solving rational equations, 390
Cartesian coordinate system, 137
Celsius-Fahrenheit relationship, 173–174
Center
of a circle, 642
of an ellipse, 644Center-radius form of a circle, 643
Change-of-base rule, 608
Circle, 642
calculator graphing of, 646, 648
center of, 642
center-radius form of, 643
equation of, 643
graph of, 642
radius of, 642
Coefficient, 34, 278
binomial, 702–703
leading, 279
numerical, 34, 278
Collinear points, 160
Columns of a matrix, 247
Combinations, 702
Combined variation, 412
Combining like terms, 34, 280
Common difference of an arithmetic
sequence, 684
Common logarithms, 604
applications of, 604
evaluating, 604
Common ratio of a geometric
sequence, 691
Commutative properties, 34–35
Complementary angles, 88
Completing the square, 499, 541
Complex conjugates, 478
Complex fraction, 380
steps to simplify, 380
Complex numbers, 476
addition of, 477
conjugates of, 478
division of, 478
imaginary part of, 476
multiplication of, 477
nonreal, 476
real part of, 476
standard form of, 476
subtraction of, 477
Composite function, 286–287
evaluating, 287
Composition of functions, 286–287
Compound inequalities, 103
withand, 103
withor, 106
Compound interest, 71, 616
continuous, 617
formula for, 530, 616
Concours d’elegance, 379
Conditional equation, 52–53
Conic sections, 635, 642
geometric interpretation of, 642
identifying by equation, 653
summary of, 652C
B
A
Index