$\"\"$

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 $\"\"$ .

$\"\"$

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 $\"\"$ .

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 intersected at $\"\"$ and $\"\"$ .

Graph :

Graph the function with its horizontal and vertical asymptotes.

$\"\"$

The zeros in the numerator is $\"\"$ and $\"\"$ .

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

$\"\"$ .

$\"\"$

\ \

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

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

$\"\"$

End behavior of the graph:

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

$\"\"$

Graph :

The graph of $\"\"$ :

$\"\"$ .

$\"\"$

The graph of the rational function $\"\"$ :

$\"\"$ .