commutative property of multiplication
The commutative property of multiplication
states that the order of the factors in a prod-
uct does not affect the product. (Section 1.4)
complementary angles (complements)
Complementary angles are two angles whose
measures have a sum of 90°. (Section 2.4
Exercises)
completing the square The process of
adding to a binomial the expression that
makes it a perfect square trinomial is called
completing the square. (Section 9.1)
complex conjugate The complex conjugate
of is (Section 8.7)
complex fraction A complex fraction is a
quotient with one or more fractions in the nu-
merator, denominator, or both. (Section 7.3)
complex number A complex number is any
number that can be written in the form ,
where aandbare real numbers and iis the
imaginary unit. (Section 8.7)
components In an ordered pair
xandyare called the components of the
ordered pair. (Section 3.1)
composite function Ifgis a function of x,
and ƒ is a function of , then
defines the composite function of ƒ and g. It
is symbolized (Section 5.3)
composition of functions The process of
finding a composite function is called com-
position of functions. (Section 5.3)
compound inequality A compound in-
equality consists of two inequalities linked
by a connective word such as andoror.
(Section 2.6)
conditional equation A conditional equa-
tion is true for some replacements of the
variable and false for others. (Section 2.1)
conic section When a plane intersects an
infinite cone at different angles, the figures
formed by the intersections are called conic
sections. (Section 11.2)
conjugate The conjugate of is
. (Section 8.5)
consecutive integers Two integers that
differ by one are called consecutive integers.
(Section 2.4 Exercises)
consistent system A system of equations
with a solution is called a consistent system.
(Section 4.1)
constant function A linear function of the
form where bis a constant, is
called a constant function. (Section 3.6)
constant of variation In the variation
equations or the
nonzero real number kis called the constant
of variation. (Section 7.6)
contradiction A contradiction is an equa-
tion that is never true. It has no solution.
(Section 2.1)
coordinate on a number line Every point
on a number line is associated with a unique
real number, called the coordinate of the
point. (Section 1.1)
coordinates of a point The numbers in an
ordered pair are called the coordinates of the
corresponding point in the plane. (Section 3.1)
Cramer’s rule Cramer’s rule uses deter-
minants to solve systems of linear equations.
(Appendix A)
cube root function The function defined
by is called the cube root func-
tion. (Section 8.1)
cubing function The polynomial function
defined by is called the cubing
function. (Section 5.3)degree of a polynomial The degree of a
polynomial is the greatest degree of any of
the terms in the polynomial. (Section 5.2)
degree of a term The degree of a term is
the sum of the exponents on the variables in
the term. (Section 5.2)
dependent equations Equations of a sys-
tem that have the same graph (because they
are different forms of the same equation) are
called dependent equations. (Section 4.1)
dependent variable In an equation relating
xandy, if the value of the variable ydepends
on the value of the variable x, then yis called
the dependent variable. (Section 3.5)
descending powers A polynomial in one
variable is written in descending powers of
the variable if the exponents on the variables
of the terms of the polynomial decrease from
left to right. (Section 5.2)
determinant Associated with every square
matrix is a real number called the determinant
of the matrix, symbolized by the entries of the
matrix placed between two vertical lines.
(Appendix A)
difference The answer to a subtraction prob-
lem is called the difference. (Section 1.2)
difference of cubes The difference of cubes,
, can be factored as. (Section 6.3)
difference of squares The difference of
squares, , can be factored as the prod-
uct of the sum and difference of two terms, or
. (Section 6.3)
direct variation yvaries directly as xif
there exists a nonzero real number (constant)
ksuch that. (Section 7.6)
discriminant The discriminant of
is the quantity under
the radical in the quadratic formula. (Sec-
tion 9.2)
distributive property of multiplication with
respect to addition (distributive property)
For any real numbers a,b, and c, the distribu-
tive property states that
and. (Section 1.4)
distance The distance between two points
on a number line is the absolute value of the
difference between the two numbers. (Sec-
tion 1.2)
domain The set of all first components
(x-values) in the ordered pairs of a relation is
called the domain. (Section 3.5)
domain of a rational equation The domain
of a rational equation is the intersection of
the domains of the rational expressions in the
equation. (Section 7.4)element of a matrix The numbers in a
matrix are called the elements of the matrix.
(Section 4.4)
elements (members) of a set The elements
(members) of a set are the objects that belong
to the set. (Section 1.1)
elimination method The elimination
method is an algebraic method used to
solve a system of equations in which the
equations of the system are combined in
order to eliminate one or more variables.
(Section 4.1)
ellipse An ellipse is the set of all points
in a plane such that the sum of the distances
from two fixed points is constant. (Sec-
tion 11.2)
empty set (null set) The empty set, de-
noted by or , is the set containing no
elements. (Section 1.1)
equation An equation is a statement that
two algebraic expressions are equal. (Sec-
tion 1.1)
equivalent equations Equivalent equations
are equations that have the same solution set.
(Section 2.1)
equivalent inequalities Equivalent inequal-
ities are inequalities that have the same
solution set. (Section 2.5)
expansion by minors A method of evalu-
ating a or larger determinant is called
expansion by minors. (Appendix A)
exponent (power) An exponent, or power,
is a number that indicates how many times
its base is used as a factor. In xis the
exponent. (Sections 1.3, 5.1)bx,3 * 356 0E
1 b+c 2 a=ba+caa 1 b+c 2 =ab+acbx+c= 0 b^2 - 4 acax^2 +y=kxx^2 - y^2 = 1 x+y 21 x-y 2x^2 - y^21 x-y 21 x^2 +xy+y^22x^3 - y^3 x^3 - y^3 =D
ƒ 1 x 2 =x^3ƒ 1 x 2 = 23 xy=kx,y=kx, y=kxz,ƒ 1 x 2 =b,a-b
a+b1 ƒg 21 x 2.g 1 x 2 ƒ 1 g 1 x 221 x,y 2 ,a+bia+bi a-bi.