$\"\"$

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 $\"\"$ .

Find which number make the fraction undefined create an equation where the

denominator is not equal to $\"\"$ .

$\"\"$

Therefore, the denominator is $\"\"$ .

$\"\"$

The domain of $\"\"$ 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.

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 $\"\"$ .

Determine the horizontal asymptotes:

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

Degree of the numerator is $\"\"$ and degree of the denominator is $\"\"$ .

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 is $\"\"$ and the real zeros of denominator is $\"\"$ .

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.

\ \

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