Glossary
G-1
For a more complete discussion, see the section(s) in parentheses.
absolute value The absolute value of a
number is the distance between 0 and the
number on a number line. (Section 1.1)
absolute value equation An absolute value
equation is an equation that involves the
absolute value of a variable expression. (Sec-
tion 2.7)
absolute value function The function de-
fined by with a graph that includes
portions of two lines is called the absolute
value function. (Section 11.1)
absolute value inequality An absolute
value inequality is an inequality that involves
the absolute value of a variable expression.
(Section 2.7)
addition property of equality The addi-
tion property of equality states that the same
number can be added to (or subtracted from)
both sides of an equation to obtain an equiva-
lent equation. (Section 2.1)
addition property of inequality The addi-
tion property of inequality states that the
same number can be added to (or subtracted
from) both sides of an inequality to obtain an
equivalent inequality. (Section 2.5)
additive inverse (negative, opposite) The
additive inverse of a number x, symbolized
is the number that is the same distance
from 0 on the number line as x, but on the
opposite side of 0. The number 0 is its own
additive inverse. For all real numbers x,
(Section 1.1)
algebraic expression Any collection of
numbers or variables joined by the basic
operations of addition, subtraction, multipli-
cation, or division (except by 0), or the
operations of raising to powers or taking roots,
formed according to the rules of algebra, is
called an algebraic expression. (Section 1.3)
annuity An annuity is a sequence of equal
payments made at equal periods of time.
(Section 12.3)
arithmetic mean (average) The arithmetic
mean of a group of numbers is the sum of all
the numbers divided by the number of num-
bers. (Section 12.1)
x+ 1 - x 2 = 1 - x 2 +x=0.
- x,
ƒ 1 x 2 =|x|A arithmetic sequence (arithmetic progres-
sion) An arithmetic sequence is a sequence
in which each term after the first differs from
the preceding term by a constant difference.
(Section 12.2)
array of signs An array of signs is used
when evaluating a determinant using expan-
sion by minors. The signs alternate for each
row and column, beginning with in the first
row, first column position. (Appendix A)
associative property of addition The as-
sociative property of addition states that the
grouping of terms in a sum does not affect
the sum. (Section 1.4)
associative property of multiplication The
associative property of multiplication states
that the grouping of factors in a product does
not affect the product. (Section 1.4)
asymptote A line that a graph more and
more closely approaches as the graph gets
farther away from the origin is called an
asymptote of the graph. (Section 7.4)
asymptotes of a hyperbola The two inter-
secting straight lines that the branches of a
hyperbola approach are called asymptotes of
the hyperbola. (Section 11.3)
augmented matrix An augmented matrix
is a matrix that has a vertical bar that sepa-
rates the columns of the matrix into two
groups, separating the coefficients from the
constants of the corresponding system of
equations. (Section 4.4)
axis (axis of symmetry) The axis of a para-
bola is the vertical or horizontal line (depend-
ing on the orientation of the graph) through
the vertex of the parabola. (Section 9.5)+boundary line In the graph of an in-
equality, the boundary line separates the
region that satisfies the inequality from the
region that does not satisfy the inequality.
(Sections 3.4, 11.5)center of a circle The fixed point that is a
fixed distance from all the points that form
a circle is the center of the circle. (Sec-
tion 11.2)
center of an ellipse The center of an ellipse
is the fixed point located exactly halfway be-
tween the two foci. (Section 11.2)
center-radius form of the equation of a cir-
cle The center-radius form of the equation
of a circle with center and radius ris
(Section 11.2)
circle A circle is the set of all points in a
plane that lie a fixed distance from a fixed
point. (Section 11.2)
coefficient(Seenumerical coefficient.)
column of a matrix A column of a matrix
is a group of elements that are read vertically.
(Section 4.4, Appendix A)
combined variation A relationship among
variables that involves both direct and inverse
variation is called combined variation. (Sec-
tion 7.6)
combining like terms Combining like terms
is a method of adding or subtracting terms
having exactly the same variable factors by
using the properties of real numbers. (Sec-
tion 1.4)
common difference The common differ-
encedis the difference between any two
adjacent terms of an arithmetic sequence.
(Section 12.2)
common logarithm A common logarithm
is a logarithm having base 10. (Section 10.5)
common ratio The common ratio ris the
constant multiplier between adjacent terms in
a geometric sequence. (Section 12.3)
commutative property of addition The
commutative property of addition states that
the order of the terms in a sum does not af-
fect the sum. (Section 1.4)1 x-h 22 + 1 y-k 22 =r^2.1 h,k 2C
base The base in an exponential expression
is the expression that is the repeated factor.
In bis the base. (Sections 1.3, 5.1)
binomial A binomial is a polynomial con-
sisting of exactly two terms. (Section 5.2)
binomial theorem (general binomial
expansion) The binomial theorem pro-
vides a formula used to expand a binomial
raised to a power. (Section 12.4)bx,