The function is
.
Step 1: Find the zeros.
\
(Set
)
(Subtract
from each side)
(Apply additive inverse property:
)
There is no zeros.
\Step 2: Find the asymptotes.
\Vertical asymptote:
\
(Set
)
(Factors)
and
(Cancl square and root terms)
and
(Simplify)
There is a vertical asymptote at
.
The degree of the denominator is greater than the degree of the numerator.
\Thus, horizontal asymptote is
.
Thus, the oblique asymptote is the line
.
Step 3: Draw the asymptotes:
\Make a table of values.
\![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
Graph:
\Graph the function
.
Plot the points obtained in the table.
\.gif\")
Graph the function
.
.gif\")