# How do you describe the end behavior for #f(x)=-x^5+4x^3-2x-2#?

##### 1 Answer

Left side up, right side down

#### Explanation:

There are two steps to describing the end behavior of a polynomial:

- Determine the behavior of the right (
#+x# "side") of the graph - Determine the behavior of the left (
#-x# "side") of the graph

**Right Side Behavior**

Determining the right side behavior of the graph involves looking at the leading coefficient, or the coefficient of the highest power of

If the leading coefficient is negative, then the right edge of the graph points downward toward the negative

For this problem, we say the right edge is pointing downward.

**Left Side Behavior**

Determining the left side behavior of the graph involves looking at the highest power of *even*, then the left side behaves the same as the right side; if that power/exponent is *odd*, then the left side behaves the opposite to the right. (I like to think the phrase *even is equal, odd is opposite* in my head.)

For this problem, the highest exponent is 5 (from

**Check with the graph**

You can verify with the graph:

graph{-x^5+4x^3-2x-2 [-3.24, 3.23, -7.12, 7.12]}