 ## Tutoring on Determining the Characteristics of Polynomial Functions

Learning Objectives:

#### Understand to Determine the Characteristics of Polynomial Functions.

Math Tutoring on Determining the Characteristics of Polynomial Functions

First, we need to understand the intercepts and turning points of polynomial functions. Sometimes these topics are referred to as short run behavior of polynomial functions. So if we are given a polynomial function of degree n, it gives us information about the graph of the polynomial function. The function has at most ‘n’    x-intercepts or horizontal intercepts, which means it also has at most n real zeros and the function has at most n - 1 turns. Let us review the end behavior or long run behavior of a polynomial function f(x) = axᵑ + ……..

The end behavior describes the value of the function or the y value as x approaches the left (-∞) and the right (+∞). The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.  Polynomial End Behavior:

1. If the degree n of a polynomial is even, then the arms of the graph are either both up or both down.

2. If the degree n is odd, then one arm of the graph is up and one is down.

3. If the leading coefficient a is positive, the right arm of the graph is up.

4. If the leading coefficient a is negative, the right arm of the graph is down.

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Hook Questions:

1.    What is a Polynomial Function?

2.    What is the Leading Coefficient test?

3.    What is the definition of a Polynomial Function?

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