MS112 Worksheet
Dr. Y. Kim
9.5 Rational Functions
)(
)(
)( xq
xp
xf =
1.
Graphs
The graph of a rational function has two or more distinct pieces (called branches) and
asymptotes.
a line which the graph approaches when we move out farther and farther along the line.
2.
Basic Graphs
•
x
k
y=,
3
x
k
y=,
5
x
k
y=, L,
7
x
k
y=
for 0
>
k for 0
<
k
•
2
x
k
y=,
4
x
k
y=,
6
x
k
y=, L,
8
x
k
y=
for 0
>
k for 0
<
k
3.
Translations
x
k
y= b
a
x
k
y+
−
=
=
=
byAH
axAV
:..
:..
shift to rt/lf by
a
up/dwn by
b
Example: The graph of 3
1
2
)( +
−
=
x
xf is shifted of
x
y2
= to right side by 1 and upward by 3.
The vertical asymptote is 1
=
x and the horizontal one is
3
=
y.
