$\"\"$

Factor the numerator and denominator of $\"\"$ .

Find the domain of the rational function :

The rational function is $\"\"$ .

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 the $\"\"$ is the set of all real numbers $\"\"$ except $\"\"$ .

The domain of function $\"\"$ is $\"\"$ .

Write $\"\"$ in lowest terms :

$\"\"$ .

So the $\"\"$ in lowest terms is $\"\"$ .

Locate the intercepts of the graph :

The rational function is $\"\"$ .

Change $\"\"$ to $\"\"$ .

$\"\"$ .

Find the intercepts.

To find $\"\"$ intercept equate the numerator $\"\"$ .

$\"\"$

Find the $\"\"$ intercept by substituting $\"\"$ $\"\"$ in the rational function.

$\"\"$

$\"\"$ intercepts are $\"\"$ and $\"\"$ intercept is $\"\"$ .

Determine the vertical asymptotes :

Find the vertical asymptote by equating denominator to zero.

$\"\"$

So the function has vertical asymptote at $\"\"$ .

Determine the horizantal 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.

Long Division Method :

$\"\"$ .

$\"\"$

Quotient is oblique asymptote.

Oblique asymptote is $\"\"$ .

$\"\"$

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

The real zero of numerator is $\"\"$ and $\"\"$ and the real zeros of denominator $\"\"$

Use these values to divide the $\"\"$ axis into four intervals.

$\"\"$ and $\"\"$ .

$\"\"$

The solid circle represent the real zeros of numerator.

The hallow circle represent the real zero of denominator.

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