Intermediate Algebra (11th edition)

interval notation Interval notation is a
simplified notation that uses parentheses
and/or brackets and/or the infinity sym-
bol to describe an interval on a number
line. (Section 1.1)

inverse of a function ƒ If ƒ is a one-to-one
function, then the inverse of ƒ is the set of
all ordered pairs of the form where
belongs to ƒ. (Section 10.1)

inverse property The inverse property for
addition states that a number added to its
opposite (additive inverse) is 0. The inverse
property for multiplication states that a num-
ber multiplied by its reciprocal (multiplicative
inverse) is 1. (Section 1.4)

inverse variation yvaries inversely as xif
there exists a nonzero real number (constant)
ksuch that. (Section 7.6)

irrational numbers An irrational number
cannot be written as the quotient of two inte-
gers, but can be represented by a point on a
number line. (Section 1.1)

joint variation yvaries jointly as xandzif
there exists a nonzero real number (constant)
ksuch that (Section 7.6)

least common denominator (LCD) Given
several denominators, the least multiple that
is divisible by all the denominators is called
the least common denominator. (Section 7.2)

legs of a right triangle The two shorter
perpendicular sides of a right triangle are
called the legs. (Section 8.3)

like terms Terms with exactly the same
variables raised to exactly the same powers
are called like terms. (Sections 1.4, 5.2)

linear equation in one variable A linear
equation in one variable can be written in the
form , where A,B,andCare
real numbers, with. (Section 2.1)

linear equation in two variables A linear
equation in two variables is an equation that
can be written in the form ,
where A,B, and Care real numbers, and A
andBare not both 0. (Section 3.1)

linear function A function defined by an
equation of the form for
real numbers aandb, is a linear function.
The value of ais the slope mof the graph of
the function. (Section 3.6)

linear inequality in one variable A linear
inequality in one variable can be written in
the form or (or
with or ), where A,B, and Care real
numbers, with. (Section 2.5)

linear inequality in two variables A lin-

ear inequality in two variables can be written

in the form or

(or with or ), where A,B, and Care

realnumbers, with AandBnot both 0. (Sec-

tion 3.4)

linear system (system of linear equations)

Two or more linear equations in two or more

variables form a linear system. (Section 4.1)

logarithm A logarithm is an exponent. The

expression represents the exponent to

which the base amust be raised to obtain x.

(Section 10.3)

logarithmic equation A logarithmic equa-

tion is an equation with a logarithm of a

variable expression in at least one term. (Sec-

tion 10.3)

logarithmic function with base a Ifaand

xare positive numbers with then

defines the logarithmic func-

tion with base a. (Section 10.3)

lowest terms A fraction is in lowest terms

if the greatest common factor of the numera-

tor and denominator is 1. (Section 7.1)

mathematical model In a real-world prob-

lem, a mathematical model is one or more

equations (or inequalities) that describe the

situation. (Section 2.2)

matrix (plural,matrices) A matrix is a

rectangular array of numbers consisting of

horizontal rows and vertical columns. (Sec-

tion 4.4, Appendix A)

minors The minor of an element in a

determinant is the determinant remain-

ing when a row and a column of the

determinant are eliminated. (Appendix A)

monomial A monomial is a polynomial

consisting of exactly one term. (Section 5.2)

multiplication property of equality The

multiplication property of equality states

that the same nonzero number can be multi-

plied by (or divided into) both sides of an

equation to obtain an equivalent equation.

(Section 2.1)

multiplication property of inequality The

multiplication property of inequality states

that both sides of an inequality may be mul-

tiplied (or divided) by a positive number

without changing the direction of the in-

equality symbol. Multiplying (or dividing)

by a negative number reverses the direction

of the inequality symbol. (Section 2.5)

multiplication property of 0 The multi-

plication property of 0 states that the product

of any real number and 0 is 0. (Section 1.4)

multiplicative inverse (reciprocal) The

multiplicative inverse (reciprocal) of a

nonzeronumberx, symbolized is the

real number which has the property that the

product of the two numbers is 1. For all

nonzero real numbers x,

(Section 1.2)

n-factorial (n!) For any positive integer n,

By definition, (Section 12.4)

natural logarithm A natural logarithm is

a logarithm having base e. (Section 10.5)

natural numbers (counting numbers) The

set of natural numbers is the set of num-

bers used for counting:

(Section 1.1)

negative of a polynomial The negative of

a polynomial is that polynomial with the

sign of every term changed. (Section 5.2)

nonlinear equation A nonlinear equation

is an equation in which some terms have

more than one variable or a variable of de-

gree 2 or greater. (Section 11.4)

nonlinear system of equations A non-

linear system of equations consists of two or

more equations to be considered at the same

time, at least one of which is nonlinear. (Sec-

tion 11.4)

nonlinear system of inequalities A non-

linear system of inequalities consists of two

or more inequalities to be considered at the

same time, at least one of which is nonlinear.

(Section 11.5)

number line A line that has a point desig-

nated to correspond to the real number 0,

and a standard unit chosen to represent the

distance between 0 and 1, is a number line.

All real numbers correspond to one and only

one number on such a line. (Section 1.1)

numerical coefficient The numerical factor

in a term is called the numerical coefficient, or

simply, the coefficient. (Sections 1.4, 5.2)

one-to-one function A one-to-one func-

tion is a function in which each x-value

corresponds to only one y-value and each

y-value corresponds to only one x-value.

(Section 10.1)

ordered pair An ordered pair is a pair of

numbers written within parentheses in the

form. (Section 3.1)

ordered triple An ordered triple is a triple

of numbers written within parentheses in the

form 1 x,y,z 2. (Section 4.2)

1 x,y 2

O

5 1, 2, 3, 4,Á 6.

0!=1.

n 1 n- 121 n- 221 n- 32 Á 122112 =n!.

N

1

x#x=x#

1

x=1.

1

x,

3 * 3

2 * 2

3 * 3

M

ƒ 1 x 2 =logax

aZ1,

logax

... Ú

Ax+By 6 C Ax+By 7 C

AZ 0

... Ú

Ax+B 6 C Ax+B 7 C

ƒ 1 x 2 =ax+b,

Ax+By=C

AZ 0

Ax+B=C

L

y=kxz.

J

y=kx

1 x,y 2

1 y,x 2

q

34

12

G-4 Glossary