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 .

The rational function is .

is in lowest terms.

The rational function is .

Change to .

.

Find the intercepts.

Find the -intercept by equating to zero.

Find the -intercept by substituting in the rational function.

-intercept is , -intercept is.

Determine the behavior of the graph of near each -intercept.

Near : .

Plot the point and indicate a line with negative slope.

Find the vertical asymptote by equating denominator to zero.

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 is and degree of the denominator is .

Since the degree of the numerator is equal to the degree of the denominator,

horizontal asymptote is the ratio of leading coefficient of numerator and

denominator.

Leading coefficient of numerator is , leading coefficient of denominator is .

is horizontal asymptote.

The function has horizontal asymptote at .

The zero of the numerator is ; the zero of denominator is ,use these values

to divide the -axis into three intervals.

and .

End behavior of the graph:

and , hence the graph of approaches

to a vertical asymptote at .

As , 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: intercept is and  -intercept is .

Step 4: The function is in lowest terms

The function has vertical asymptote at .

Step 5: The function has horizontal asymptote at ; not intersected.

Step 6:

 Step 7 and step 8:

The graph of :