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**40 POINTS** PLEASE HELP, EXPLAIN WELL IN DETAIL PLEASE DON'T COPY OTHER ANSWERS OFF THE WEB AS NONE OF THEM HAVE MADE SENSE

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.

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PsychicPhantom
Wilson and Alexis can both by correct if the the function is a parabola. It can have zeroes at points x=-1, and x=1. Thus, the average rate of change between the two points would be zero because the y values do not change as they are both zero. In this way, Wilson is correct. Alexis can be correct because the parabola can have it's highest point at its vertex between the two points. It would count as a turning point because the function would increase and then decrease again. 


Hope this helps :)
FriendToDino
If the function is a parabola, with vertex on x= 0, then the average rate of change of the function on {x: -1<x<1} is 0, because the graph is symmetric. There is also a turning point at the vertex.
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