exponential equation An exponential equa-
tion is an equation that has a variable in at least
one exponent. (Section 10.2)
exponential expression A number or let-
ter (variable) written with an exponent is an
exponential expression. (Section 1.3)
exponential function with base a An expo-
nential function with base ais a function of the
form where and for
all real numbers x. (Section 10.2)
extraneous solution A proposed solution
to an equation, following any of several pro-
cedures in the solution process, that does
not satisfy the original equation is called an
extraneous solution. (Section 8.6)
factor Ifa,b, and crepresent numbers and
thenaandbare factors of c.
(Section 1.3)
factoring Writing a polynomial as the pro-
duct of two or more simpler polynomials is
called factoring. (Section 6.1)
factoring by grouping Factoring by group-
ing is a method of grouping the terms of a
polynomial in such a way that the polynomial
can be factored. It is used when the greatest
common factor of the terms of the polynomial
is 1. (Section 6.1)
factoring out the greatest common factor
Factoring out the greatest common factor is
the process of using the distributive property
to write a polynomial as a product of the
greatest common factor and a simpler poly-
nomial. (Section 6.1)
finite sequence A finite sequence has a
domain that includes only the first npositive
integers. (Section 12.1)
first-degree equation A first-degree (lin-
ear) equation has no term with the variable
to a power other than 1. (Section 2.1)
foci (singular, focus) Foci are fixed points
used to determine the points that form a
parabola, an ellipse, or a hyperbola. (Sec-
tions 11.2, 11.3)
FOIL FOIL is a mnemonic device which
represents a method for multiplying two bino-
mials. Multiply First terms
ac,Outer terms ad,Inner terms bc, and Last
terms bd. Then combine like terms. (Section 5.4)
formula A formula is an equation in which
variables are used to describe a relationship
among several quantities. (Section 2.2)
function A function is a set of ordered pairs
in which each value of the first compo-
nentxcorresponds to exactly one value of
the second component y. (Section 3.5)
function notation If a function is denoted
by f, the notation is called function no-
tation. Here, represents the value
of the function at x. (Section 3.6)
fundamental rectangle The asymptotes of
a hyperbola are the extended diagonals of
its fundamental rectangle, with corners at
the points and
(Section 11.3)
future value of an annuity The future value
of an annuity is the sum of the compound
amounts of all the payments, compounded to
the end of the term. (Section 12.3)general term of a sequence The expression
which defines a sequence, is called the
general term of the sequence. (Section 12.1)
geometric sequence (geometric progres-
sion) A geometric sequence is a sequence
in which each term after the first is a con-
stantmultiple of the preceding term. (Sec-
tion 12.3)
graph of a number The point on a num-
ber line that corresponds to a number is its
graph. (Section 1.1)
graph of an equation The graph of an
equation in two variables is the set of all
points that correspond to all of the ordered
pairs that satisfy the equation. (Section 3.1)
graph of a relation The graph of a relation
is the graph of its ordered pairs. (Section 3.5)
greatest common factor (GCF) The
greatest common factor of a list of integers
is the largest factor of all those integers. The
greatest common factor of the terms of a
polynomial is the largest factor of all the
terms in the polynomial. (Section 6.1)
greatest integer function The function
defined by where the symbol
is used to represent the greatest integer
less than or equal to x, is called the greatest
integer function. (Section 11.1)horizontal line test The horizontal line
test states that a function is one-to-one if
every horizontal line intersects the graph of
the function at most once. (Section 10.1)
hyperbola A hyperbola is the set of all
points in a plane such that the absolute value
of the difference of the distances from two
fixed points is constant. (Section 11.3)
hypotenuse The hypotenuse is the longest
side in a right triangle. It is the side opposite
the right angle. (Section 8.3)identity An identity is an equation that is
true for all valid replacements of the vari-
able. It has an infinite number of solutions.
(Section 2.1)
identity element for addition For all real
numbers The num-
ber 0 is called the identity element for
addition. (Section 1.4)
identity element for multiplication For
all real numbers a, The
number 1 is called the identity element for
multiplication. (Section 1.4)
identity function The simplest polynomial
function is the identity function, defined by
(Section 5.3)
identity property The identity property
for addition states that the sum of 0 and any
number equals the number. The identity
property for multiplication states that the
product of 1 and any number equals the
number. (Section 1.4)
imaginary part The imaginary part of a
complex number is b. (Section 8.7)
imaginary unit The symbol i, which repre-
sents is called the imaginary unit.
(Section 8.7)
inconsistent system An inconsistent sys-
tem of equations is a system with no solution.
(Section 4.1)
independent equations Equations of a
system that have different graphs are called
independent equations. (Section 4.1)
independent variable In an equation relat-
ingxandy, if the value of the variable yde-
pends on the value of the variable x, then xis
called the independent variable. (Section 3.5)
index (order) In a radical of the form
nis called the index or order. (Section 8.1)
index of summation When using summa-
tionnotation, the letter iis called
the index of summation. Other letters can be
used. (Section 12.1)
inequality An inequality is a statement that
two expressions are not equal. (Section 1.1)
infinite sequence An infinite sequence is
a function with the set of all positive integers
as the domain. (Section 12.1)
integers The set of integers is. (Section 1.1)
intersection The intersection of two sets
AandB, written , is the set of elements
that belong to both A and B. (Section 2.6)
interval An interval is a portion of a
number line. (Section 1.1)
A ̈B- 2,-1, 0, 1, 2, 3,Á 6
5 Á,-3,an
i= 1ƒ 1 i 2 ,2 na,2 - 1 ,a+biƒ 1 x 2 =x.a# 1 = 1 #a=a.
a,a+ 0 = 0 +a=a.I
H
xƒ 1 x 2 = x,an,G
1 a,-b 2.1 a,b 2 , 1 - a,b 2 , 1 - a,-b 2 ,y=ƒ 1 x 2ƒ 1 x 21 x,y 2
1 a+b 21 c+d 2a#b=c,
F
ƒ 1 x 2 =ax, a 70 aZ 1