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 fir the function between, x=-2 and x=2, the graph goes through a turning point and back down. Explain how Hunter and Maggie can both be correct, using complete sentences.

Question

jim_thompson5910 · Answer

Were you able to get anywhere with this?

anonymous · Answer

Nope

jim_thompson5910 · Answer

The average rate of change formula is 

$$\Large A = \frac{f(x_1)-f(x_2)}{x_1-x_2}$$

If A = 0, then $\Large f(x_1)-f(x_2) = 0$ which means that $\Large f(x_1) = f(x_2)$

jim_thompson5910 · Answer

So if the average rate of change from x = -2 to x = 2 is 0, then f(-2) = f(2)

jim_thompson5910 · Answer

Now if "the graph goes through a turning point and back down", then we know that f(-2) starts off low and as x increases, y increases. This happens until we hit a turning point (let's say in the midpoint) and then come back down to x = 2

So it might look something like this

|dw:1389744092860:dw|