$\"\"$

\

\

The rational function is $\"\"$ .

\

\

The function can be written as $\"\"$ or $\"\"$ .

\

Find the Intercepts.

\

The function is $\"\"$ .

\

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

\

$\"\"$ .

\

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

\

$\"\"$ .

\

The numerator has no real zeros, so there is no $\"\"$ intercept.

\

\

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 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 $\"\"$ .

\

Degree of the denominator is greater than Degree of the numerator, So Horizantal asymptote is $\"\"$ .

\

So the function has horizantal asymptote at $\"\"$ .

\

\

The function is $\"\"$ .

\

There are holes at $\"\"$ and $\"\"$ because the original function is undefined when $\"\"$ .

\

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 $\"\"$ .

\

$\"\"$

\

No $\"\"$ intercept.

\

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

\

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

\

The function has horizantal asymptote at $\"\"$ .

\

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

\

Graph the function $\"\"$ . \ \

\

$\"\"$