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Math 1310
Section 4.4
Rational Functions
•
The objective in this section will be to identify the important features of a rational
function and then to use them to sketch an accurate graph of the function.
A rational function is a function of the form
)
(
)
(
)
(
x
Q
x
P
x
f
=
where both
)
(
x
P
and
)
(
x
Q
are
polynomial functions and
.
0
)
(
≠
x
Q
An example of a polynomial function is
9
4
3
)
(
2
2



=
x
x
x
x
f
.
The features you will want to identify are:
•
the locations of any holes in the graph of the function
•
the locations of any vertical or horizontal asymptotes
•
the locations of any
x
or
y
intercepts
•
the behavior of the function on either side of each vertical asymptote and each
zero of the function
If you do not have enough information from these features, you may need to graph a
point or two to help you sketch the functions.
We’ll start by finding the locations of any asymptotes and any holes for the graph of the
function.
To do so,
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 Summer '08
 MARKS
 Rational Functions

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