**of a polynomial function.**

*3 key features***#1:**The

**of a polynomial function can be used to**

*degree***. How?**

*determine the finite differences***A polynomial function of**

*General Rule:***degree “n”**(“n” is a

*positive integer*, the

*and have the*

**“nth” differences are constant****.**

*same sign as the leading coefficient***Example #1:** f(x)=2 x^3 +5

- The degree is
**3**, which means the.**3rd finite differences will be constant** - The
, which means the 3rd finite differences are*leading coefficient (2) is positive*.*positive*

**Example #2:** f(x)= -5 x^24 +2

- The degree is
**24**, which means the.*24th differences will be constant* - The
, which means the 24th differences are*leading coefficient (-5) is negative*.*negative*

** That is, for example, if a function has a degree of 123, you do not need to calculate 123 finite differences using the table of values! All you need to do is look at the degree and the leading coefficient to determine when the differences are constant (in this case in the 123rd differences) and if it is positive or negative.*

**#2:** You can classify a function as ** increasing** or

**.**

*decreasing*a. **The graph rises from left to right** - increasing

b. **The graph falls from left to right** - decreasing

For example:

**When writing in interval notation, make sure you include "xE" in front of the brackets!*

**A**

*#3:***is used to describe the point where the function**

*turning point***from**

*changes***(or vice-versa).**

*increasing to decreasing*Some new terminologies:

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