INDEX
A
C
Absolute value, 13
equation, 104
function, 173
inequality, 106
ac method, 306
Addition
of complex numbers, 430
of polynomials, 278
of radical expressions, 407
of rational expressions, 350
of real numbers, 15
of signed numbers, 16
Addition method, 209
Addition property of equality, 55
Addition property of inequality, 87
Additive identity, 34
Additive inverse, 15
Algebraic expression, 26
Amount formula, 271
Annuity, 648
Arithmetic expression, 23
Arithmetic sequence, 638
common difference, 638
nth term, 638
sum of terms, 640
Arithmetic series, 640
Associative properties, 32
Asymptotes, 603
Augmented matrix, 225
Average rate of change, 169
Axis of symmetry, 584
Cartesian coordinate system, 122
Center, 593
Change of base, 559
Circle, 593
equation of, 593
Coefficient, 39, 275
Column, 224
Combined variation, 513
Combining like terms, 39
Commission problems, 79
Common base, 530
Common difference, 638
Common logarithm, 542
Common ratio, 643
Commutative properties, 32
Completing the square, 449
Complex conjugates, 432
Complex fraction, 358
Complex number, 429
addition, 430
conjugates, 432
division, 431
imaginary part, 429
multiplication, 431
real part, 429
subtraction, 430
Composition, 493
Compound inequality, 94
Compound interest, 535
Conditional equation, 58
Conic sections, 580
circle, 593
ellipse, 600
hyperbola, 602
parabola, 580
Conjugates, 410
complex, 432
Consecutive integers, 73
Constant, 275
Constant function, 172
Constant of variation, 510
Constant term, 275
Constraints, 244
Continuous-compounding
formula, 536
B
Base, 258
Base-change formula, 559
Basic principle of rational
numbers, 335
Binomial, 276
expansion, 652
square of, 284
Binomial theorem, 653
Branches, 603
Building up the denominator, 337
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Index
Coordinate, 9
Coordinate system, 122
Counting numbers, 2
Cramer’s rule, 231, 240
Cube root, 389
Cubed, 24
D
Degree, 276
Denominator
least common, 56, 351
rationalizing, 401
Dependent equations, 202
Dependent variable, 124, 165
Determinants, 231
expansion by minors, 238
minor, 237
Diagonal of a matrix, 226
Difference, 23
Difference of two cubes, 300
Difference of two real numbers, 23
Difference of two squares, 299
Direct variation, 510
Directly proportional, 510
Directrix, 580
Discriminant, 461
Distance, 424
Distance formula, 424
Distributive property, 33
Dividend, 19, 289
Division
of complex numbers, 431
definition, 19
of polynomials, 290
of radical expressions, 413
of rational expressions, 345
of real numbers, 19
of signed numbers, 19
synthetic, 291
by zero, 20
Divisor, 19, 289
Domain, 166
Domain of a rational expression, 334
E
e, 530
Element
of a matrix, 224
of a set, 2
Elimination method, 217
Ellipse, 600
focus, 600
Empty set, 4
Entry, 224
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Equal sets, 2
Equality
addition property of, 55
multiplication property of, 55
Equation, 54
absolute value, 104
conditional, 58
dependent, 202
equivalent, 55
exponential, 534
with exponents, 418
identity, 58
inconsistent, 58
independent, 202
linear, 59, 124
literal, 65
logarithmic, 544
nonlinear, 572
quadratic, 316
quadratic in form, 467
with radicals, 418
with rational exponents, 423
with rational expressions, 365
root, 54
solution, 54
systems of, 200
Equations of a line
point-slope form, 141
slope-intercept form, 143
standard form, 143
Equivalent equations, 55
Equivalent inequalities, 88
Equivalent matrices, 225
Evaluating expressions, 23
Evaluating polynomials, 276
Even root, 388
Even-root property, 419
Expansion by minors, 238
Exponent, 24
base, 24
definition, 24
integral, 258
negative, 258
positive, 258
power rules, 268
product rule, 259
quotient rule, 262
rational, 390
rules for, 271
zero, 260
Exponential equation, 534
Exponential expression, 24, 258
Exponential function, 530
Expression, 23
algebraic, 26
arithmetic, 23
Textbook Table of Contents
Index
exponential, 24
radical, 398
rational, 334
Extraneous root, 366
Extraneous solution, 366
Extremes, 367
Extremes-means property, 368
square root, 175
sum, 492
vertical line test, 177
Fundamental rectangle, 603
G
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Factor, 17
greatest common, 296
Factor theorem, 518
Factorial, 653
Factoring, 292
ac method, 306
completely, 296
the difference of two cubes, 300
the difference of two squares, 299
the greatest common factor, 297
by grouping, 305
perfect square trinomials, 299
polynomials, 296
by substitution, 301
the sum of two cubes, 300
summary of methods, 313
trial-and-error, 307
trinomials, 305
with variable exponents, 302
Factoring out, 296
Finite sequence, 628
Finite set, 2
f-notation, 167
Focus, 580
FOIL method, 283
Formula, 65
Fourth root, 388
Function, 164
absolute value, 173
composition of, 493
constant, 172
difference, 492
exponential, 443
identity, 172
inverse, 499
linear, 146, 171
logarithmic, 541
maximum value of, 175
minimum value of, 175
notation, 167
one-to-one, 500
operations, 492
polynomial, 277
product, 492
quadratic, 174
quotient, 492
rational, 338
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Gaussian elimination method, 226
Geometric problems, 76
Geometric sequence, 643
common ratio, 643
nth term, 643
sum of terms, 646
Geometric series, 645
infinite, 647
sum of n terms, 646
Graph, 9, 123
of circle, 593
of ellipse, 600
of hyperbola, 602
of inequality, 85
of line, 124
of parabola, 580
Graphing, 123
Greater than, 84
Greatest common factor, 296
Grouping, factoring by, 305
Grouping symbols, 23
H
Horizontal line, 125
Horizontal line test, 501
Hyperbola, 602
asymptotes, 603
branches, 603
focus, 602
fundamental rectangle, 603
Hypotenuse, 319
I
i, 429
Identity, 58
additive, 34
multiplicative, 34
Identity function, 172
Identity properties, 34
Imaginary number, 429
Inconsistent equation, 58
Inconsistent system, 202
Independent, 202
Independent variable, 124, 165
Index, 398
Index of summation, 634
Inequality, 84
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Index
Linear systems
in three variables, 217
in two variables, 200
Linear systems, solution of
addition method, 209
applications, 204
determinant method, 231
elimination method, 217
graphing method, 200
substitution method, 202
Literal equation, 65
Logarithm, 541
changing the base, 559
common, 542
definition, 541
inverse properties, 551
natural, 542
power rule, 550
product rule, 548
quotient rule, 549
Logarithmic equations, 544
Logarithmic function, 541
Lowest terms, 335
Inequality (cont.)
absolute value, 106
addition property, 87
compound, 94
equivalent, 88
linear, 87, 151
multiplication property, 87
quadratic, 473
rational, 476
second-degree, 610
simple, 94
symbols, 84
systems of, 200
Infinite geometric series, 647
Infinite sequence, 628
geometric, 643
Infinite set, 2
Integers, 8
consecutive, 73
Integral exponents, 258
Intercepts, 125
Interest, 66
Intersection of sets, 4
Interval notation, 85
Inverse
additive, 15
multiplicative, 18, 35
Inverse of a function, 499
Inverse properties, 35
Inverse variation, 511
Inversely proportional, 511
Invertible function, 500
Investment problems, 77
Irrational numbers, 10
M
J
Joint variation, 512
Jointly proportional, 512
L
Lambert, Johann Heinrich, 10
Leading coefficient, 276
Least common denominator, 56, 351
Least common multiple, 351
Legs, 319
Less than, 84
Like radicals, 407
Like terms, 39
Line segment, 130
Linear equation, 59, 124
Linear function, 146
Linear inequality, 87, 151
Linear polynomial, 298
Linear programming, 244
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Matrix, 224
Maximum value, 175
Means, 367
Members of a set, 2
Midpoint formula, 130
Minimum value, 175
Minor, 237
Mixture problems, 78
Model, 73
Monomial, 276
Multiplication
of complex numbers, 431
of polynomials, 279
of radical expressions, 408
of rational expressions, 343
of real numbers, 17
Multiplication property
of equality, 55
of inequality, 87
of zero, 36
Multiplicative identity, 34
Multiplicative inverse, 18, 35
N
Natural base, 530
Natural logarithms, 542
Natural numbers, 2
Negative exponent, 258
Net worth, 15
Nonlinear equation, 572
Textbook Table of Contents
Index
Odd root, 389
Odd-root property, 419
One-to-one function, 500
Opens downward, 175
Opens upward, 175
Operation, order of, 25
Opposites, 14
Or, in compound inequalities, 94
Order of a matrix, 224
Order of operations, 25
Ordered pair, 122
Ordered triple, 217
Origin, 9
monomial, 276
multiplication, 279
prime, 310
quadratic, 298
subtraction, 278
term of, 275
trinomial, 276
Polynomial function, 277
Positive exponents, 258
Power of a power rule, 268
Power of a product rule, 269
Power of a quotient rule, 269
Power rule for logarithms, 550
Power rules, 268
Power rules for exponents, 268
Present-value formula, 272
Prime number, 296
Prime polynomial, 301
Principal nth root, 388
Principal square root, 24
Principle of linear programming, 245
Product, 17, 23
Product of signed numbers, 18
Product rule for exponents, 259
Product rule for logarithms, 548
Product rule for radicals, 398
Properties of equality, 55
Properties of inequality, 87
Properties of logarithms, 548
Properties of real numbers, 47
Proportion, 367
Proportional, 510
Proportionality constant, 510
Pythagorean theorem, 319
P
Q
Parabola, 175, 580
vertex, 175, 580
Parallel lines, 135
Pascal’s triangle, 652
Perfect cube, 403
Perfect square, 399
Perfect square trinomial, 299
Perpendicular lines, 135
pH, 547
Pi, 10
Plotting points, 123
Point-slope form, 141
Polynomial, 275
addition, 278
binomial, 276
degree, 276
division, 290
evaluating, 276
factoring, 292
linear, 298
Quadrant, 122
Quadratic equation, 316
summary of solution methods, 460
Quadratic formula, 458
discriminant, 461
Quadratic function, 398
Quadratic in form, 467
Quadratic inequality, 473
Quadratic polynomial, 298
Quotient, 19, 23, 289
Quotient rule for exponents, 262
Quotient rule for logarithms, 549
Quotient rule for radicals, 399
Nonlinear systems of equations, 572
Notation, scientific, 263
Notation, set-builder, 2
nth root, 388
principal, 388
Number line, 9
Numbers
complex, 429
counting, 2
imaginary, 429
integers, 8
irrational, 10
natural, 2
prime, 296
rational, 8
real, 10
signed, 16
whole, 7
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R
Radical, 397
Radical equations, 418
Radical expression, 398
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Index
Radical expression (cont.)
adding, 407
dividing, 413
multiplying, 408
subtracting, 407
Radical notation, 397
Radical symbol, 24
Radicals, simplifying, 401
Radicand, 398
Radius, 593
Range, 166
Rational exponents, 390
Rational expression, 334
addition, 350
building up, 337
complex fraction, 358
division, 345
domain, 334
least common denominator, 351
multiplication, 343
reducing, 335
subtraction, 350
Rational function, 339
Rational inequalities, 476
Rational numbers, 8
basic principle, 335
Rationalizing the denominator,
401, 415
Reading a graph, 28
Real numbers, 10
addition, 15
division, 19
multiplication, 17
subtraction, 17
Reciprocal, 18
Rectangular coordinate system, 122
Relation, 165
Remainder, 290
Removing parentheses, 42
Rise, 131
Root
cube, 389
of an equation, 54
even, 388
extraneous, 366
fourth, 388
nth, 388
odd, 389
principal, 388
square, 24, 388
Row, 224
Row operations, 226
Rules for exponents, 271
Rules for radicals
product, 398
quotient, 399
Run, 131
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S
Satisfying an equation, 54
Scientific notation, 263
Second-degree inequality, 610
Sequence, 628
arithmetic, 638
finite, 628
general term, 628
geometric, 643
infinite, 628
nth term, 628
term of, 628
Series, 634
arithmetic, 640
finite, 635
geometric, 645
infinite geometric, 647
Set, 2
elements of, 2
empty, 4
equal, 2
finite, 2
infinite, 2
intersection, 4
members of, 2
solution, 54
subset, 4
union, 3
Set notation, 2
Set-builder notation, 2
Sets, equal, 2
Sign array, 238
Sign graph, 473
Signed numbers, 16
Simple inequality, 94
Simple interest, 68
Simplified radical form, 401
Simplifying radicals, 401
Slope, 131
Slope-intercept form, 143
Solution of an equation, 54
Solution set, 54, 85
Solving equations, 55
Solving for a specified variable, 65
Solving inequalities, 87
Solving word problems, 76
Special products, 286
Square of a binomial, 284
Square root, 24
of a negative number, 433
Squared, 24
Square-root function, 175
Standard form, 143
Subscript, 27
Subset, 4
Substitution method, 202
Textbook Table of Contents
Index
Substitution, method of factoring
by, 301
Subtraction
of complex numbers, 430
definition, 17
of polynomials, 278
of radical expressions, 407
of rational expressions, 350
of real numbers, 17
of signed numbers, 17
Sum, 23
of arithmetic series, 640
of geometric series, 646
of infinite geometric series, 647
of real numbers, 15
of signed numbers, 16
of two cubes, 300
Summation notation, 634
Switch-and-solve strategy, 502
Symbols of inequality, 84
Symmetric about y-axis, 584
Synthetic division, 291
System of equations, 200
dependent, 202
inconsistent, 202
independent, 202
linear, 200
nonlinear, 572
in three variables, 217
in two variables, 200
System of inequalities, 612
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Taking a square root, 388
Taking an nth root, 388
Term, 39, 275
like, 39
Term of a sequence, 628
Test points, 154, 478
Translating words into algebra, 75
Trial and error, 307
Trichotomy property, 90
Trinomial, 276
factoring, 305
perfect square, 299
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U
Undefined, 20
Uniform motion problems, 374
Union of sets, 3
Unit, 9
V
Variable, 2
dependent, 124
independent, 124
solving for a specified, 65
Variation, 510
Variation constant, 510
Varies directly, 510
Varies inversely, 511
Varies jointly, 512
Venn diagram, 3
Vertex, 175, 580
Vertical line, 125
Vertical line test, 177
W
Whole numbers, 7
Word problems, 75
Work problems, 374
X
x-axis, 122
x-coordinate, 122
x-intercept, 125
xy-plane, 122
Y
y-axis, 122
y-coordinate, 122
y-intercept, 125
Z
Zero exponent, 260
Zero factor property, 316
Zero of a function, 517
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