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 :

First determine the intervals of , such that the graph is above the -axis and where from the graph.

The graph of the function is above the -axis and on the intervals .

From the graph,  for  or .

The solution set is  or in interval notation, .

; .