Conjugate
of a binomial, 461
of a complex number, 478
Consecutive integers, 88
Consistent system, 212
Constant function, 193
Constant of variation, 407
Consumer Price Index (CPI), 526
Continuous compounding, 617
formula for, 617
Contradiction, 52–53
Coordinate(s)
on a line, 3
of points in a plane, 137
of a point, 3
Coordinate system
Cartesian, 137
rectangular, 137
Cost-benefit equation, 611
Cost-benefit model, 379
Counting numbers, 2, 5
Cramer’s rule, 718–719
derivation of, 717
Creating linear models, 166–169
Cross products, 398
Cube(s)
difference of, 335, 337, 340
of a number, 24
sum of, 336–337, 340
Cube root function, 430
graph of, 430
Cubing function, 289
Data modeling, 166
Decay
applications of, 584–585
exponential, 584–585, 618
Decibel, 606
Decimals, linear equations with, 51
Degree
of a polynomial, 279
of a term, 278
Denominator
least common, 372
rationalizing, 459
Dependent equations, 212
solving a system of, 217
Dependent variable, 181–182
Descartes, René, 136
Descending powers, 279
Determinant of a square matrix, 715
array of signs for, 717
evaluating, 715, 717
expansion by minors, 716
minor of, 716
Difference, 15
Difference of cubes, 335, 340
factoring of, 335
Difference of squares, 340
factoring of, 333
Dimensions of a matrix, 247
Direct variation, 407
as a power, 409
Discriminant, 508, 544
Distance, 17
Distance, rate, time relationship, 82, 237,
398
Distance between points, 17
formula for, 449
Distance to the horizon formula, 434, 452
Distributive property, 32, 50
Division
of complex numbers, 478
of polynomial functions, 305
of polynomials, 302
of rational expressions, 367
of real numbers, 19
synthetic, 724
by zero, 19
Domain
agreement on, 186
of a function, 184
of a rational equation, 386
of a rational function, 362, 389
of a relation, 184
Double negative property, 6
Doubling time, 610
Downward opening parabola, 534e, 606
Elements of a matrix, 247
Elements of a set, 2
symbol for, 2
Elimination method for solving systems,
215–216, 659
Ellipse
apogee of, 649
calculator graphing of, 646, 648
center of, 644
equation of, 644
foci of, 644
graph of, 645
intercepts of, 644
perigee of, 649
perimeter of, 672
Empty set, 2
notation for, 2
Equality
addition property of, 49
multiplication property of, 49
Equation(s), 8, 48
absolute value, 113
of a circle, 642
conditional, 52–53
contradiction, 52–53
dependent, 212
distinguishing from expressions, 68
of an ellipse, 644
equivalent, 49
exponential, 582, 613first-degree, 48, 139
graph of, 139
of a horizontal line, 140, 164
of a hyperbola, 650
identity, 52–53
independent, 212
of an inverse function, 574
linear in one variable, 48
linear in three variables, 226
linear in two variables, 139
linear system of, 210, 226
literal, 57
with no solution, 387
nonlinear, 48, 657
polynomial, 343
power rule for, 468
quadratic, 344, 496
quadratic in form, 515
with radicals, 468
rational, 386
with rational expressions, 386
second-degree, 496
solution of, 48
translating words into, 68
of a vertical line, 140, 164
Equilibrium price, 663
Equivalent equations, 49
Equivalent forms of fractions, 20
Equivalent inequalities, 92
Euclid, 84
Euclidean geometry, 84
Euler, Leonhard, 608
Expansion of a determinant by minors, 716
Exponential decay, 584–585, 618
Exponential equations, 582, 613
applications of, 616
calculator graphing method for solving,
619
general method for solving, 614
properties for solving, 582, 613
steps to solve, 583
Exponential expressions, 24
base of, 24
evaluating, 25
simplifying, 270
Exponential functions, 580
applications of, 584
characteristics of graph of, 582
converting to logarithmic form, 588
graphs of, 580–582
properties of, 598
Exponential growth, 584, 618
Exponential notation, 24, 435
Exponents, 24, 264
base of, 24, 264
fractional, 435
integer, 264
negative, 265
power rules for, 268
product rule for, 264
quotient rule for, 267