plot the graph of f(X)=2x^2+6x+4
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Find where the expression
2
x
2
+
5
2
(
3
x
−
2
)
is undefined.
x
=
2
3
Consider the rational function
R
(
x
)
=
a
x
n
b
x
m
where
n
is the degree of the numerator and
m
is the degree of the denominator.
1. If
n
<
m
, then the x-axis,
y
=
0
, is the horizontal asymptote.
2. If
n
=
m
, then the horizontal asymptote is the line
y
=
a
b
.
3. If
n
>
m
, then there is no horizontal asymptote (there is an oblique asymptote).
Find
n
and
m
.
n
=
2
m
=
1
Since
n
>
m
, there is no horizontal asymptote.
No Horizontal Asymptotes
Find the oblique asymptote using polynomial division.
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y
=
x
3
+
2
9
This is the set of all asymptotes.
Vertical Asymptotes:
x
=
2
3
No Horizontal Asymptotes
Oblique Asymptotes:
y
=
x
3
+
2
9
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