Learning Objectives:

__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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