College Algebra 9th txtbk

I-6 SUBJECT INDEX
Linear models, construction of, 149–151
Linear regression
examples of, 152–154
explanation of, 151
Linear systems. See Systems of linear equations
Line graph, 57
Lines
equations of, 132, 133, 137–140, 158
graphs of, 132–133
horizontal, 139, 140
parallel, 141–142
perpendicular, 141–142
regression, 153
slope-intercept form of, 137–138
slope of, 134–136
vertical, 139, 140, 166
Line segment
length of, 66
midpoint of, 124–126
Location theorem, 280–281
Logarithmic equations
explanation of, 372, 380
method to solve, 375–376
Logarithmic-exponential conversions, 356–357
Logarithmic-exponential relationships, 360–361
Logarithmic functions
change-of-base formula and, 361–362
conversions of, 356–357
explanation of, 329, 354, 379–380
graphs of, 354–356
properties of, 358–359, 380
Logarithmic models
applications of, 380
data analysis and regression, 369
logarithmic scales, 365–369
Logarithmic scales, 365–369
Logarithms
common, 359, 360
on graphing calculator, 359–361, 370
natural, 359, 360
Logistic growth, 350
Logistic models, 349
Long division
explanation of, 5
polynomial, 266–267
Lower triangular matrix, 571
Lowest terms, 32–33
Magnitude, 367
Mathematical induction
examples of, 513–517
explanation of, 512–513, 564
extended principle of, 517
principle of, 512
Mathematical models
applications of, 230–231, 242–243
explanation of, 147–148
exponential, 340–350
polynomial, 271–273, 285
quadratic, 210–211, 214–215
Matrices
addition of, 457–458
applications of, 460–462, 464–465
augmented, 443–445, 447
column, 461–462
decoding, 482
explanation of, 442–443, 497
Gauss-Jordan elimination and, 447–451, 475
on graphing calculators, 442, 458, 473, 488
identity, 470–471
inverse methods to solve linear systems, 498
inverse of square, 471–473
lower triangular, 571
multiplication of, 459–466
negative of, 458
principal diagonal of, 442
properties of, 477
reduced, 444–447
row, 442, 461–462
row-equivalent, 444, 474
singular, 472
size of, 442
square, 442
subtraction of, 458–459
upper triangular, 495, 571
zero, 458
Matrix equations
explanation of, 477
method to solve, 477–478
systems of linear equations and, 478–480
Midpoint, of line segment, 124–126
Midpoint formula
explanation of, 124
use of, 125–126
Minor of element, in third-order determinant, 489
Mixture problems, 52–53
Models. See Mathematical models
Monomials, 22. See also Polynomials
Multiplication
associative property of, 4, 6
commutative property of, 4, 6
of complex numbers, 76–78
identity matrix for, 470–471
of matrices, 459–466
of polynomials, 24
of rational expressions, 33–34
of real numbers, 3–7
Multiplication principle
application of, 533–534
explanation of, 532–533, 565
Multiplication properties
of equality, 45
of matrices, 477
of real numbers, 6
Multiplicative identity, 4, 78
Multiplicative inverse, 4, 6, 11, 471–472
Multiplicities
from graphs, 292
of zero, 289, 291, 292
Multiplier doctrine, 527
Napierian logarithms. See Natural logarithms
Nappes, of cone, 386n
Natural logarithms, 359, 360
Natural numbers, 2, 79
Negative growth, 342
Negative real numbers
explanation of, 3
principal square root of, 80
properties of, 7, 8
n factorial, 534–535
Nonrepeating linear factors, 587–588
Nonrigid transformations, 193
Notation/symbols
absolute value, 65
composition of function, 226, 228