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Name
Section 9.2 Graphing Simple and Rational Functions
Date
PD
Goal: Graph simple rational functions
1)
2)
3)
The examples above are known as rational functions. Rational functions take the form
p(x) and q(x) polynomials and
will learn more about these next year).
where
We describe the graph of rational functions as hyperbolas (you
Every general hyperbola,




has the following properties:
,
The x-axis is a horizontal asymptote.
The y-axis is a vertical asymptote.
The domain and range are all nonzero real numbers.
The graph has two symmetrical parts called branches. For each point (x, y) on one branch, there is a
corresponding point (-x, -y) on the other branch.
All rational functions of the form
and
have graphs that are hyperbolas with asymptotes at
.
Practice: Find the vertical (
) and horizontal (
and range. Then graph the function by hand.
) asymptotes of the following. State the domain
To graph:
 Use a dotted line to represent the asymptotes.
 Plot a couple of points on each side of the vertical asymptote.
 Draw the branches approaching the asymptotes.
1)
y
1
2
x3
2) y 
2
3
x4
Functions of the form
are also hyperbolas, have a vertical asymptote at the x-value that makes
the denominator zero, and a horizontal asymptote at
Practice: Find the asymptotes of the following functions, state the domain and range, and sketch each
graph.
1) y 
x2
3x  4
2) y 
 4x
8
x5
3) y 
x 1
2x  4
4) y 
 3x
2
6x  1