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Example 6 from Algebra and Trigonometry, 5.2 Power Functions and Polynomial Functions
Identifying End Behavior and Degree of a Polynomial Function
Describe the end behavior and determine a possible degree of the polynomial function in Figure 7.
Figure
7
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
As the input values get very large, the output values increase without bound. As the input values get very small, the output values decrease without bound. We can describe the end behavior symbolically by writing
In words, we could say that as values approach infinity, the function values approach infinity, and as values approach negative infinity, the function values approach negative infinity.
We can tell this graph has the shape of an odd degree power function that has not been reflected, so the degree of the polynomial creating this graph must be odd and the leading coefficient must be positive.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Describe the end behavior, and determine a possible degree of the polynomial function in Figure 8.
Figure
8
How did it go?