$\"\"$

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

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 :

$\"\"$ .

$\"\"$ 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 :

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 quotient of the leading coefficient of the numerator is $\"\"$ , and the leading coefficient

of the denominator, $\"\"$ .

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

Find out whether the graph of $\"\"$ intersects the asymptote, solve the equation for $\"\"$ .

$\"\"$ .

The graph intersects the line $\"\"$ at $\"\"$ $\"\"$ .

$\"\"$

Use the zeros of the numerator and denominator of $\"\"$ to divide

the $\"\"$ -axis into intervals:

The real zero of numerator are $\"\"$ 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.

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

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