Question

Two students in your class, Hunter and Maggie, are disputing a function. Hunter says that for the function, between x = –2 and x = 2, the average rate of change is 0. Maggie says that for the function, between x = –2 and x = 2, the graph goes up through a turning point, and then back down. Explain how Hunter and Maggie can both be correct, using complete sentences.

Answer 1

@uri

Answer 2

thank you

Answer 3

yes

Answer 4

ill help u again gaby

Answer 5

The function has the same value at x = -2 and x = +2 (in order for the average rate of change to be zero, the function must have the same value at x = -2 and x = 2 ). So at x = -2, the function is either increasing (as in the first figure) or decreasing (as in the second figure). In either case it means the function has to turn somewhere in between to get back to the same value at B.

The only time Maggie can be wrong and Hunter can be right is when the function is a horizontal line passing through A and B, in which case there won't be any turning point. But they are only asking how they can both be right and the explanation in the previous paragraphs would explain that.