PLEASE HELP ME UNDERSTAND THIS !

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.

Question

PLEASE HELP ME UNDERSTAND THIS !

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.

tkhunny · Answer

Pick ANY symmetric function on [-1,1] with the properties stated by Alexis.  Make sure it get's back to where it started.

anonymous · Answer

but I dont understand a single thing about this x;

tkhunny · Answer

That's why you must pick a function - any function with the properties stated by Alexis.  ANY!!

$y = 1 - |x|$

$y = -x^{2} + 1$

$y = \dfrac{1}{x^{2}+1}$

$y = \cos(x)$

Just to name a few.