The rational function is .

Factorize the numerator and denominator .

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The domain of the function is all possible values of .

The denominator of the function should not be zero.

and .

The domain of the is the set of all real numbers except  and .

The domain of function is .

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There are no common factors between the numerator and denominator, is in lowest terms.

The rational function is .

Find the intercepts.

Find the - intercepts by equating .

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-intercept is .

Determine the behavior of the graph of near each -intercept.

Near : .

Plot the point and indicate a line with negative slope.

Find the -intercept by substituting in .

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-intercept is .

The rational function is .

Find the vertical asymptote by equating denominator to zero.

The function has vertical asymptotes at and .

Find the horizontal or oblique asymptote.

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Here the degree of the numerator is greater than denominator, so the function will have oblique asymptote.

Degree of the numerator is and degree of the denominator is .

The quotient is .

Oblique asymptote is .

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Oblique asymptote intersected the graph at .

The zeros of the numerator are ;the zeros of the denominator are .

Use these values to divide the axis into four intervals.

, , and .

Interval	\ \	\ \	Location of graph	\ \
\ \	\ \	\ \	\ Below \ -axis \	\ \
\ \	\ \ \	\ \ \	\ Above \ -axis \	\ \
\ \	\ \	\ \	\ Below \ -axis \	\ \
	\ \	\ \	\ Above \ -axis \	\ \

End behavior of the graph:

and .

and .

The Rational function has oblique asymptote is .

Graph :

The graph of :

Step 1: ; Domain of is .

Step 2: is in lowest terms.

Step 3: intercept: ; -intercepts: .

Step 4: is in lowest terms; vertical asymptotes: and .

Step 5: Oblique asymptote is , intersected at .

Step 6:

Interval	\ \	\ \	Location of graph	\ \
\ \	\ \	\ \	\ Below \ -axis \	\ \
\ \	\ \ \	\ \ \	\ Above \ -axis \	\ \
\ \	\ \	\ \	\ Below \ -axis \	\ \
	\ \	\ \	\ Above \ -axis \	\ \

Step 7 and step 8:

Graph of :

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