$\"\"$

The rational function is $\"\"$ .

In rational functions the denominator can not be zero.

To find exceptional values equate denominator to zero.

$\"\"$

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

$\"\"$ .

Now $\"\"$ is in lowest terms.

The rational function is $\"\"$ .

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

$\"\"$ .

Find the intercepts.

To find $\"\"$ -intercept equate numerator to $\"\"$ .

The function has no $\"\"$ -intercept.

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

$\"\"$ .

The $\"\"$ -intercept is $\"\"$ .

Find the vertical asymptote by equating denominator to zero.

$\"\"$

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

Graph :

Graph the function with its horizontal and vertical 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 is $\"\"$ .

Since the degree of the numerator $\"\"$ and degree of the denominator is $\"\"$ , the horizontal asymptote occurs at $\"\"$ and not intersected.

The horizontal asymptote is $\"\"$ .

$\"\"$

There are no zeros in the numerator.

The zeros of denominator are $\"\"$ and $\"\"$ , use these values to divide the $\"\"$ axis into three intervals.

$\"\"$ .

$\"\"$

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