(a).

The function is .

Graph of the function is :

.

(b).

Leading term test for polynomial end behavior :

The end behavior of any non-constant polynomial function can be described in one of the following four ways, as determined by the degree of the polynomial and its leading coefficient .

For odd and positive :

and .

For odd and negative :

and .

For even and positive :

and .

For even and negative :

and .

The polynomial function is .

The degree is and the leading coefficient is .

Since the degree is (even) and the leading coefficient is (positive), the end behavior of the graph of is and .

(a).

Graph of the function is :

(b). and .