The function is .

Determine the end behavior of the graph of the function.

The function is .

The polynomial function is of degree .

The leading coefficient is .

The graph of behave like for large values of .

Graph the function using graphing utility.

Graph :

Draw a coordinate plane.

Graph the function .

Use a graphing utility to approximate the and - intercepts of the graph.

Observe the graph of the function :

The graph touches the -axis at and .

Thus, the - intercepts are and .

The graph touches the -axis at .

Thus, the - intercept is .

Use a graphing utility to create a table to find points on the graph around each - intercept.

Observe the graph of the function :

The points , , and are on the graph of .

Table :

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Approximate the turning points of the graph.

Since the degree of the function is , it has at most turning points.

Observe the graph of the function :

The graph has a turning point at and .

Put all the information from the steps 1 through step 5 together to obtain graph of :

Graph :

Graph the function .

Plot the turning point at and .

Plot the points , and .

Determine the domain and range of the function :

Observe the graph of the function :

Domain of the function is set of all real number which makes the function mathematically correct.

Domain is all real numbers.

Range is the set of the output of the function.

Range is all real numbers.

Use the graph to determine where the function is increasing and where it is decreasing :

Observe the graph of the function :

The graph is increasing on the interval and .

The graph is decreasing on the interval .

Step 1 : .

Step 2 :

Graph the function :

Step 3 :

- intercepts : and .

- intercept : .

Step 4 :

Table :

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Step 5 :

Turning point is and .

Step 6 :

Graph of the function :

.

Step 7 :

Domain : .

Range : .

Step 8 :

Increasing on and .

Decreasing on .