$\"\"$

\

The rational function is $\"\"$ .

\

Find the intercepts.

\

The function is $\"\"$ .

\

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

\

$\"\"$ .

\

To find $\"\"$ intercept, substitute $\"\"$ in the function.

\

$\"\"$

\

$\"\"$

\

$\"\"$ intercept is $\"\"$ .

\

To find $\"\"$ -intercept, substitute $\"\"$ in the function.

\

$\"\"$

\

$\"\"$ intercept is $\"\"$ .

\

\

Find the vertical asymptotes.

\

Find the vertical asymptotes by equating denominator to zero.

\

$\"\"$

\

The function has vertical asymptotes at $\"\"$ .

\

Find the horizantal asymptote.

\

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 $\"\"$ .

\

The ratio of the leading coefficients of numerator and denominator are equal,and the degree of polynomial are equal $\"\"$ is horizontal asymptote.

\

The function has horizontal asymptote is $\"\"$ .

\

\

The function is $\"\"$ .

\

Graph :

\

Draw the coordinate plane.

\

Graph the function $\"\"$ .

\

$\"\"$

\

\

Find the domain.

\

The function is $\"\"$ .

\

The domain of a function is the set of all real numbers which makes the function mathematically correct.

\

Denominator of the function should not be $\"\"$ .

\

$\"\"$ \ \

\

Thus, the function is continuous for all real numbers except $\"\"$ .

\

Therefore, domain of the function is $\"\"$ . \ \

\

$\"\"$

\

$\"\"$ intercept is $\"\"$ .

\

$\"\"$ intercept is $\"\"$ .

\

The function has vertical asymptotes at $\"\"$ .

\

The function has horizontal asymptote is $\"\"$ .

\

Domain of the function is $\"\"$ . \ \

\

Graph of the function $\"\"$ is

\

$\"\"$