Question

Two students in your class, Wilson and Alexis, are disputing a function. Wilson says that for the function, between x = -1 and x = 1, the average rate of change is 0. Alexis says that for the function, between x = -1 and x = 1, the graph goes up through a turning point, and then back down. Explain how Wilson and Alexis can both be correct, using complete sentences.

Answer 1

I do not understand what kind of answer they are looking for. Also, what would this graph look like?

Answer 2

Have you considered \(f(x) = \dfrac{1}{1+x^{2}}\)?

Answer 3

No, where did you get that?

Answer 4

"Explain how Wilson and Alexis can both be correct, using complete sentences."

You will need an example. I just gave you one. Next time, you will know one.

Answer 5

So this can be an example of what the graph would be? And then I can plot it and see what both of them are trying to say?

Answer 6

Yes. That is exactly what you can do. If you want a similar argument...

1) The average rate of change is zero
2) It decreases to a turning point and goes back up.

You can use \(g(x) = e^{x} + e^{-x}\)

Really, anything symmetric about the y-axis would be helpful to examine.

Answer 7

Okay thank you so much. :) I'll see what I can do.

Answer 8

Go get 'em!