The function is .

Factor the numerator and denominator of . Find the domain of rational function.

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The domain of a rational function is the set of all real numbers except those for which the denominator is .

To find which number make the fraction undefined create an equation where the denominator is not equal to .

The domain of is .

Write in lowest terms:

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Locate the intercepts of the graph and determine the behavior of the graph of near each - intercept :

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Change to .

Find the intercepts :

Find the -intercept by equating the numerator to zero.

-intercept is .

Find the -intercept by substituting in the .

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-intercept is .

Determine the vertical asymptotes :

Find the vertical asymptote by equating denominator to zero.

There is no vertical asymptote .

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The function not defined at .

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Hole at .

Determine the horizontal asymptotes / oblique asymptotes:

To find horizontal asymptote, first find the degree of the numerator and degree of the denominator.

Degree of the numerator and degree of the denominator .

Since the degree of the numerator is greater than degree of denominator, there is no horizontal asymptote.  

Find oblique asymptote.

Oblique asymptote is found by long division.

Quotient is oblique asymptote.  

Oblique asymptote is .  

intersected all points except .

Use the zeros of the numerator and denominator of to divide the -axis into intervals: 

Real zeros of the numerator is at  and .

Real zeros of the denominator is at .

Use these values to divide the -axis into three intervals.

, , and .

Interval	\ \	\ \
\ Number chosen \	\ \	\ \
\ Value of \	\ \	\ \	\ \
\ Location of graph \	\   \ Below \ -axis \   \	\ Below \ -axis   \	\ Above \ -axis  \
\ Point of graph \	\ \	\ \	\ \

The graph of is above the -axis for .

The graph of does not intersect the graph of horizontal asymptote at . Therefore the graph of will approach from .

The graph of is below the -axis for  .

Since the graph of is above the -axis for and intersect the graph of oblique asymptote at , the graph of will approach from .

Use the results obtained in Steps 1 through 7 to graph the function :

The graph of :

1: 

The domain of is .

2: .

3: -intercept is and -intercept is .

4: Vertical asymptote : none.

Hole at .

5: Oblique asymptote is at intersected all points except .

6:

Interval	\ \	\ \
\ Number chosen \	\ \	\ \
\ Value of \	\ \	\ \	\ \
\ Location of graph \	\   \ Below \ -axis \   \	\ Below \ -axis   \	\ Above \ -axis  \
\ Point of graph \	\ \	\ \	\ \

7 and 8:

The graph of :

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