$\"\"$

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 of $\"\"$ except $\"\"$ and $\"\"$ .

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

Write $\"\"$ in lowest terms :

$\"\"$ .

$\"\"$

$\"\"$ 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.

$\"\"$

$\"\"$ intercept is $\"\"$ , $\"\"$ intercept is $\"\"$ .

Determine the vertical asymptotes :

Find the vertical asymptote by equating denominator to zero.

$\"\"$

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

Hole at $\"\"$ .

Determine the horizantal 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 equal to the degree of the denominator, horizontal asymptote is the ratio of leading coefficient of numerator and denominator.

The graph of $\"\"$ has the horizontal asymptote at $\"\"$ .

$\"\"$

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

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

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

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

$\"\"$

The solid circle represent the real zeros of numerator.

The hallow circle represent the real zeros of denominator.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

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