1
Lesson 30
Section 6.1
Rational Expressions and Functions
A
Rational Expression
is a polynomial divided by a nonzero polynomial.
The following are examples of rational expressions.
8
5
2
,
1
3
,
5
9
,
2
,
4
3
2
2
2

+

+

+
y
y
y
r
r
r
x
x
w
A
Rational Function
is a function where
f
(
x
) is represented by a rational expression.
1)
Evaluate the following rational function for the given values.
5
1
3
)
(
2

+

=
x
x
x
x
G
for
x
= 0, 2, 3, and 5
Remember:
No fraction (rational expression can have a zero denominator.
When a
rational expression or rational function has a single variable, the set of numbers that
could be replaced for that variable is called the
domain.
No number can be included in
the domain that makes a zero denominator when replaced for
x
(or the variable).
When
these numbers are determined, it is said these are the
domain restrictions
.
For each rational expression or rational function, list all domain restrictions.
2
4
( )
3
2
( )
(
3)(
5)
2
( )
(
4)(
4)
x
A
r x
x
x
x
B
f x
x
x
x
C
g x
x
x
x
x
+
=
≠
=
≠
+

=
≠
+

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 Spring '09
 Rational Expressions, Division, Fraction, Elementary arithmetic, Rational function, rational expression

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