Rewrite the rational function in the form , where is a polynomial and is an integer.

Match each rational function with its end behavior as  gets larger and larger in the positive and negative directions. (Note: Some of the answer choices are not used, and some answer choices are used more than once.)

Let the function be defined by . Mai divides by and gets:

For the polynomial function , we have  ,  . Rewrite as a product of linear factors.

There are many cones with a volume of cubic inches. The height , in inches, of one of these cones is a function of its radius , in inches, where .

1. What is the height of one of these cones if its radius is 2 inches?
2. What is the height of one of these cones if its radius is 3 inches?
3. What is the height of one of these cones if its radius is 6 inches?

A cylindrical can needs to have a volume of 10 cubic inches. There needs to be a label around the side of the can. The function gives the area of the label in square inches, where is the radius of the can in inches.

1. As gets closer and closer to 0, what does the behavior of the function tell you about the situation?

2. As gets larger and larger, what does the end behavior of the function tell you about the situation?

Match each rational function with a description of its end behavior as gets larger and larger.