$\"\"$

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 $\"\"$ .

$\"\"$

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.

Find $\"\"$ intercept equate the numerator to $\"\"$ .

$\"\"$

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

$\"\"$

$\"\"$ intercepts are $\"\"$ ,No $\"\"$ intercept.

Determine the vertical asymptotes:

Find the vertical asymptote by equating denominator to zero.

$\"\"$

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

Determine the horizantal asymptotes:

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 is $\"\"$ .

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

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

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

$\"\"$

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