Section 3.7 Rational Functions
A
rational function
,
R
, is a function of the form
R
(
x
)=
p
(
x
)
q
(
x
)
where
p
(
x
)
,q
(
x
) are polynomials.
Example.
R
(
x
x
+1
x
+2
is a rational function.
Example.
R
(
x
x
2
+3
x

1
x
4
+3
x
2

2
x
is a rational function.
Example.
f
(
x
√
x
is not a rational function.
Example.
f
(
x
)=sin
x
is not a rational function.
The domain of a rational function,
f
(
x
p
(
x
)
q
(
x
)
, is the set of all
x
such that
q
(
x
)
6
=0.
Example.
The domain of
r
(
x
x
+1
x

2
is (
∞
,
2)
∪
(2
,
∞
).
The graph of
f
(
x
1
x
is shown below.
–10
–5
0
5
10
–3
–2
–1
1
2
3
y
=
1
x
The graph of
f
(
x
1
x

2
is shown below.
–10
–5
0
5
10
1234
y
=
1
x

2
The graph of
f
(
x
1
x
2
is shown below.
–10
–5
0
5
10
–3
–2
–1
1
2
3
y
=
1
x
2
The graph of
f
(
x
1
(
x

2)
2
is shown below.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document0
10
20
1234
y
=
1
(
x

2)
2
The line of
y
=
L
is a
horizontal asymptote
of the graph of
y
=
f
(
x
)i
f
f
(
x
)
→
L
as
x
→∞
or if
f
(
x
)
→
L
as
x
→∞
.
Example.
The line
y
= 0 is a horizontal asymptote of the graph of
y
=
1
x
.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '11
 Kutter
 Algebra, Polynomials, Rational Functions, Rational function

Click to edit the document details