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 .

Consider .

Factorize the denominator in above expression.

.

is in lowest terms.

The rational function is .

Change to .

.

Find the intercepts.

Find the -intercept by equating to zero.

Above expression cannot be zero.

Therefore there is no -intercept to .

Find the -intercept by substituting in the rational function.

- intercept is.

Find the vertical asymptote by equating denominator to zero.

The function has vertical asymptote, that is .

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 .

Since the degree of numerator is less than degree of denominator so is

a proper rational function, and the graph of will have the horizontal

asymptote .

The function has horizontal asymptote at .

There are no zeros of the numerator; the zeros of denominator are ,

use these values to divide the axis into three intervals.

and .

End behavior of the graph:

As and , hence the graph of approaches

to a vertical asymptote at .

As and, hence the graph of approaches

to a vertical asymptote at .

As and , hence the graph of approaches

to a horizontal asymptote at .

Graph :

The graph of :

Step 1: ; Domain of function is .

Step 2: The rational function in lowest terms .

Step 3: There is no -intercepts, -intercept is .

Step 4: The function in lowest terms.

The function has vertical asymptote at .

Step 5: Horizontal asymptote is , not intersected.

Step 6: \ \

Step 7 and Step 8:

Graph of :