Question

I am VERY confused to even know how to begin to solve this problem. I need someone to walk me through this problem. Medal as always.



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

@ganeshie8 @Hero @Nnesha @iambatman much appreciation.

Answer 2

both can be wrong eh hun or nah ?

Answer 3

Well I'm not sure, it just says explain how both of them ~could~ be correct.

For this should I use my knowledge of graphing functions and translation meanings or something different?

Answer 4

ohh nvm i thought both x are positive hm

Answer 5

well
if slope is zero you will draw horizontal line

Answer 6

do you have graph with this question or table ?

Answer 7

No there is no graph or table.

Answer 8

i will use slope formula
(average rate of change - slope )\[\huge\rm \frac{ y_2 - y_1}{ x_2 -x_1 }\]
if slope is 0 then you should get 0 at the numerator

substitute x's values x=1 and x=-1

Answer 9

What about Alexis?

Answer 10

Alexis says that for the function, between x = -1 and x = 1, the graph goes up through a turning point, and then back down.

goes up through a turning point, then back down? ?

Answer 11

well how would you get 0 at the numerator
in order to get zero both y values should be the same
like y_1 = 2 y_2 = 2
then you will get 0 \[\frac{ 2-2 }{ 1-(-1) } = \frac{ 0 }{ 2}\]
when slope is zero you will draw horizontal line
x values are increasing but y's is constant