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?