Hyperbola, 650
asymptotes of, 650
equations of, 650
foci of, 650
fundamental rectangle of, 651
graph of, 650–651
intercepts of, 650
steps to graph, 651
Hypotenuse of a right triangle, 448
i, 474
powers of, 479
Identity elements, 33
Identity equations, 52–53
Identity function, 288–289
Identity properties, 33
Imaginary part of a complex number, 476
Imaginary unit, 474
Incidence rate, 393
Inconsistent system, 212, 230, 251
solving, 217
Independent equations, 212
Independent variable, 181–182
Index
of a radical, 428
of summation, 680
Inequalities, 8
absolute value, 113
addition property of, 92
compound, 103
equivalent, 92
interval notation for, 10
linear in one variable, 91
linear in two variables, 175
multiplication property of, 94
nonlinear, 552
nonlinear system of, 665
polynomial, 555
quadratic, 552
rational, 555
second-degree, 664
summary of symbols, 9
symbols for, 8–9
system of, 665
three-part, 11, 96
Infinite geometric sequence, 696
sum of terms of, 696
Infinite sequence, 678
terms of, 678
Infinite set, 2
Infinity symbol, 10
Integer exponents, 264
Integers, 3
consecutive, 88
Intercepts
of an ellipse, 644
of a hyperbola, 650
of a parabola, 544
x-, 139
y-, 139, 162
Interest
compound, 71, 530, 616
simple, 57, 71, 616
unearned, 64
Intersection
of linear inequalities, 177
of sets, 103
Interval notation, 9–11, 91
Interval on a number line, 9–11
Inverse
additive, 6, 34
multiplicative, 18, 34
of a one-to-one function, 572
Inverse of a function, 572
calculator graphing method to find, 576
definition of, 572
equation of, 574
graph of, 575–576
steps to find the equation of, 574
symbol for, 572
Inverse properties, 34
Inverse variation, 409
as a power, 409
Irrational numbers, 4, 5
Isosceles triangle, 453Joint variation, 411Leading coefficient, 279
Leading term, 279
Least common denominator (LCD), 372
steps to find, 372
Legs of a right triangle, 448
Less than, 8–9
definition of, 8
Light-year, 277
Like terms, 34, 280
combining, 34, 280
Limit notation, 696
Line(s)
horizontal, 140
number, 3
slope of, 148
vertical, 140–141
Line graph, 136
Line segment, midpoint of, 142
Linear equation in one variable, 48
applications of, 67, 81
calculator graphing method for solving,
169
with decimals, 51
with fractions, 51
solution of, 48
solution set of, 48, 97
solving, 48
steps to solve, 50
types of, 53
Linear equations in three variables, 226
graphs of, 227Linear equations in two variables, 139
graph of, 138
point-slope form of, 163
slope-intercept form of, 161
standard form of, 139, 164
summary of forms of, 166
system of, 210, 226
x-intercept of, 139
y-intercept of, 139, 162
Linear function, 193, 289
definition of, 193
Linear inequalities in one variable, 91
applications of, 97
with fractions, 96
solution sets of, 97
steps to solve, 95
three-part, 96
Linear inequalities in two variables, 175
boundary line of graph, 175
calculator graphing of, 178
graph of, 175
intersection of, 177
region of solution, 175
union of, 178
Linear models, creating, 166–169
Linear programming, 181
Linear system of equations.SeeSystem of
linear equations
Literal equation, 57
Lithotripter, 649
Logarithmic equations, 589
calculator graphing method for solving,
619
properties for solving, 613
solving, 614
steps to solve, 616
Logarithmic functions, 588
applications of, 592
with base a, 590
characteristics of graph of, 591
converting to exponential form, 588
graphs of, 590
properties of, 598
Logarithms, 588
alternative forms of, 599
change-of-base rule for, 608
common, 604
definition of, 588
evaluating, 604
exponential form of, 588
natural, 606
power rule for, 597
product rule for, 595
properties of, 590, 595, 599
quotient rule for, 596
LORAN, 673
Lowest terms of a rational expression, 363Mapping of sets, 183
Mathematical expressions from words, 67