Section 2.3 – Rational Functions
1
Section 2.3
Rational Functions and Their Graphs
A
rational function
can be expressed as
)
(
)
(
)
(
x
q
x
p
x
f
=
where
p
(
x
) and
q
(
x
)
are
polynomial functions and
q
(
x
)
≠
0.
Vertical Asymptote of Rational Functions
The line
x = a
is a
vertical asymptote
of the graph of a function
f
if
f
(
x
) increases or
decreases without bound as
x
approaches
a
.
Example:
Given the graph of
x
x
f
1
)
(
=
.
Locating Vertical Asymptotes and Holes
Factor the numerator and denominator.
Look at each factor in the denominator.
•
If a factor cancels with a factor in the numerator, then there is a hole where that
factor equals zero.
•
If a factor does not cancel, then there is a vertical asymptote where that factor
equals zero.
Example 1:
Find any vertical asymptotes and/or holes of
6
10
3
)
(
2
2




=
x
x
x
x
x
f
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentSection 2.3 – Rational Functions
2
Horizontal Asymptote of Rational Functions
The line
y = b
is a
horizontal asymptote
of the graph of a function
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Staff
 Rational Functions, Limit of a function, Rational function

Click to edit the document details