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IM Alg2.2.19 Practice: End Behavior of Rational Functions

The function  can be rewritten in the form . What is the end behavior of ?

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

Match each polynomial with its end behavior as x 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: How could we tell by looking at the remainder that  is a factor?

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

What is the height of one of these cones if its radius is 3 inches?

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

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 x gets larger and larger.