relation A relation is a set of ordered
pairs. (Section 3.5)
rise Rise refers to the vertical change
between two points on a line—that is, the
change in y-values. (Section 3.2)
row echelon form If a matrix is written
with 1s on the diagonal from upper left to
lower right and 0s below the 1s, it is said to
be in row echelon form. (Section 4.4)
row of a matrix A row of a matrix is a
group of elements that are read horizontally.
(Section 4.4, Appendix A)
row operations Row operations are opera-
tions on a matrix that produce equivalent
matrices, leading to systems that have the
same solutions as the original system of
equations. (Section 4.4)
run Run refers to the horizontal change
between two points on a line—that is, the
change in x-values. (Section 3.2)
scientific notation A number is written in
scientific notation when it is expressed in
the form , where and
nis an integer. (Section 5.1)
second-degree inequality A second-degree
inequality is an inequality with at least one
variable of degree 2 and no variable with
degree greater than 2. (Section 11.5)
sequence A sequence is a function whose
domain is the set of natural numbers or a set
of the form (Section 12.1)
series The indicated sum of the terms of a
sequence is called a series. (Section 12.1)
set A set is a collection of objects. (Sec-
tion 1.1)
set-builder notation The special symbol-
ism has a certain property is called
set-builder notation. It is used to describe a
set of numbers without actually having to list
all of the elements. (Section 1.1)
signed numbers Signed numbers are num-
bers that can be written with a positive or
negative sign. (Section 1.1)
simplified radical A simplified radical
meets four conditions:
- The radicand has no factor (except 1)
raised to a power greater than or equal to
the index. - The radicand has no fractions.
- No denominator contains a radical.
- Exponents in the radicand and the index
of the radical have 1 as their greatest com-
mon factor.
(Section 8.3)
slope The ratio of the change in yto the
change in xfor any two points on a line is
called the slope of the line. (Section 3.2)
slope-intercept form A linear equation is
written in slope-intercept form if it is in the
form , where mis the slope and
is the y-intercept. (Section 3.3)
solution of an equation A solution of an
equation is any replacement for the variable
that makes the equation true. (Section 2.1)
solution set The solution set of an equa-
tion is the set of all solutions of the equation.
(Section 2.1)
solution set of a linear system The solution
set of a linear system of equations consists of
all ordered pairs that satisfy all the equations
of the system at the same time. (Section 4.1)
solution set of a system of linear inequali-
ties The solution set of a system of linear
inequalities consists of all ordered pairs that
make all inequalities of the system true at
the same time. (Section 11.5)
square matrix A square matrix is a matrix
that has the same number of rows as
columns. (Section 4.4, Appendix A)
square of a binomial The square of a bi-
nomial is the sum of the square of the first
term, twice the product of the two terms, and
the square of the last term. That is,
and. (Section 5.4)
square root The inverse of squaring a
number is called taking its square root. That
is, a number ais a square root of kif.
(Section 1.3)
square root function The function defined
by with is called the
square root function. (Sections 8.1, 11.3)
square root property The square root
property (for solving equations) states that
if , then or.
(Section 9.1)
squaring function The polynomial func-
tion defined by is called the
squaring function. (Section 5.3)
standard form of a complex number The
standard form of a complex number is
. (Section 8.7)
standard form of a linear equation A lin-
ear equation in two variables written in the
form , with AandBnot both 0,
is in standard form. (Sections 3.1, 3.3)
standard form of a quadratic equation
A quadratic equation written in the form
, where a,b, and care
real numbers with , is in standard
form. (Sections 6.5, 9.1)
step function A function that is defined
using the greatest integer function and has a
graph that resembles a series of steps is called
a step function. (Section 11.1)
substitution method The substitution
method is an algebraic method for solving a
system of equations in which one equation is
solved for one of the variables, and then the
result is substituted into the other equation.
(Section 4.1)
sum The answer to an addition problem is
called the sum. (Section 1.2)
sum of cubes The sum of cubes, ,
can be factored as. (Section 6.3)
summation (sigma) notation Summation
notation is a compact way of writing a series
using the general term of the corresponding
sequence. It involves the use of the Greek
letter sigma,. (Section 12.1)
supplementary angles (supplements) Sup-
plementary angles are two angles whose
measures have a sum of 180°. (Section 2.4
Exercises)
synthetic division Synthetic division is a
shortcut procedure for dividing a polynomial
by a binomial of the form. (Appendix B)
system of equations A system of equa-
tions consists of two or more equations to be
solved at the same time. (Section 4.1)
system of inequalities A system of ineq-
ualities consists of two or more inequalities
to be solved at the same time. (Section 11.5)
term A term is a number, a variable, or
the product or quotient of a number and one
or more variables raised to powers. (Sec-
tions 1.4, 5.2)
term of an annuity The time from the be-
ginning of the first payment period to the
end of the last period is called the term of an
annuity. (Section 12.3)
terms of a sequence The function values
in a sequence, written in order, are called
terms of the sequence. (Section 12.1)
three-part inequality An inequality that
says that one number is between two other
numbers is called a three-part inequality.
(Section 2.5)
trinomial A trinomial is a polynomial con-
sisting of exactly three terms. (Section 5.2)union The union of two sets AandB, writ-
ten , is the set of elements that belong
toeither A or B(or both). (Section 2.6)A ́BU
T
x-kg1 x^2 - xy+y^22x^3 +y^3 = 1 x+y 2 #
x^3 +y^3aZ 0ax^2 +bx+c= 0Ax+By=Ca+biƒ 1 x 2 =x^2x^2 =k x= 2 k x=- 2 kƒ 1 x 2 = 2 x, xÚ0,a^2 =kx^2 - 2 xy+y^21 x+y 22 =x^2 + 2 xy+y^21 x-y 22 =1 0,b 2y=mx+b5 x|x 65 1, 2, 3,Á,n 6.a* 10 n 1 ...|a| 610