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 .

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

Graph : 

Determine the domain and range of the function :

Observe the graph of the function :

Domain is all real numbers.

Range is .

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 .

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 :

.

Step 6 :

Graph of the function :

.

Step 7 :

Domain : .

Range : .

Step 8 :

Increasing on .

Decreasing on .