Mathematical model, 56
Matrix (matrices), 247, 715
augmented, 247
calculator display of, 247
columns of, 247
dimensions of, 247
elements of, 247
reduced row echelon form of, 253
row echelon form of, 248
row operations on, 248
rows of, 247
square, 247, 715
Matrix method for solving systems,
248–251
Maximum value of a quadratic function,
545
Mean, arithmetic, 681
Members of a set, 2
Midpoint of a line segment, 142
formula for, 142
Minimum value of a quadratic function,
545
Minor of a determinant, 716
Mixture problems, 73, 236–237
Model(s), 166
to approximate data, 285
mathematical, 56
quadratic functions as, 526, 535
Money problems, 81, 235
Monomials, 279
multiplication of, 293
Motion problems, 82–83, 237–238,
398–400, 513
Multiplication
associative property of, 34–35
of binomials, 294, 458
commutative property of, 34–35
of complex numbers, 477
FOIL method of, 295, 458
identity element for, 33
identity property of, 33
inverse property of, 34
of monomials, 293
of polynomial functions, 298
of polynomials, 293
of radical expressions, 458
of radicals, 443
of radicals with different indexes, 447
of rational expressions, 366
of real numbers, 17
of sum and difference of two
terms, 296
using logarithms, 595
by zero, 18, 36
Multiplication property
of equality, 49
of inequality, 94
of zero, 36
Multiplicative identity, 33
Multiplicative inverse of a real number,
18, 34
Napier, John, 601
Natural logarithms, 606
applications of, 607
evaluating, 607
Natural numbers, 2, 5
Negative
of a number, 6
of a polynomial, 281
Negative exponents, 265
definition of, 265
in rational expressions, 383
rules for, 267, 269
Negative nth root, 428
Negative root, 428
Negative slope, 152
Negative square root, 26
Newton, 408
nfactorial, 702
Nonlinear equation, 48, 657
Nonlinear system of equations, 657
calculator graphing method for
solving, 661
elimination method for solving, 659
substitution method for solving, 658
Nonlinear system of inequalities, 665
graph of, 666
Nonreal complex number, 476
Not equal to, 2
symbol for, 2
Notation
exponential, 24, 435
factorial, 702
function, 190
interval, 9–11, 91
limit, 696
scientific, 271–272
set, 2
set-builder, 2
sigma, 680
square root, 26, 428
subscript, 142
summation, 680
nth root, 428
exponential notation for, 435
Null set, 2
notation for, 2
Number(s)
absolute value of, 6–7, 431
additive inverse of, 6, 34
complex, 476
counting, 2, 5
cubes of, 24
factors of, 24
graph of, 3
imaginary, 476
integers, 3
irrational, 4–5
natural, 2, 5
negative of, 6nonreal complex, 476
opposite of, 6
ordered pair of, 136
pure imaginary, 476
rational, 4–5
real, 4–5
reciprocal of, 18
roots of, 428
sets of, 2
signed, 6
square roots of, 25, 428
squares of, 24
whole, 2, 5
Number line, 3
coordinate of a point on, 3
distance between points, 17
graph of a point, 3
intervals on, 9
Numerator, rationalizing, 463
Numerical coefficient, 34, 278Ohm’s law, 481
One-to-one function, 572
horizontal line test for, 573
inverse of, 572
Operations
on functions, 285, 298, 305
order of, 26
on real numbers, 14–20
on sets, 103, 105
Opposite of a number, 6
Order
of operations, 26
of a radical, 428
Ordered pairs, 136
graph of, 137
table of, 138
Ordered triple, 226
Ordinary annuity, 695
future value of, 695
payment period of, 695
Origin, 136Pairs, ordered, 136
Parabola, 289, 349, 531
applications of, 545–546
axis of, 531, 534, 546
graph of, 531, 546
graphing by calculator, 349, 353
horizontal, 546
horizontal shift of, 533
intercepts of, 544
summary of graphs of, 548
symmetry of, 531
vertex formula for, 542
vertex of, 531, 534, 541, 546
vertical, 532
vertical shift of, 533
Parallel lines, slope of, 152, 165