Question

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
-3x5 + 9x4 + 5x3 + 3

Answer 1

What do you think?

Answer 2

-3x5?

Answer 3

Yes correct

Answer 4

3?

Answer 5

Idk, I'm confused.

Answer 6

Since n is odd and a is negative the end behavior is up and down

Answer 7

3 = odd

Answer 8

Where did you get n and a from?

Answer 9

n = 3

a = -3

Answer 10

Oh okay, so how do we find the end behavior?

Answer 11

Great link that describes end behavior

https://www.youtube.com/watch?v=PbSJHr-fg7I

Answer 12

Ok, can you still help me with the question? @Nixy

Answer 13

As you plugin positive numbers for x what happens? If you start with 0 for x the graph will go up but since we have a - for a and and odd for n (3) it will first go up starting at 0 and then it will start going down at some point. That is why the answer is

Since n is odd and a is negative the end behavior is up and down

Answer 14

So as x -> infinity, it will go up and then down

Answer 15

So the end behavior is....?

Answer 16

Up and down?