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

so basically, if it goes up then back down to the same level, the change is 0 since it is like, running 100 feet west, then running 100 feet east, you are at your original spot, your positino did not change

maggie is explaing what hunter is saying

Answer 2

consider an example
`f(x)=-x^2+4`

Explanation:

hunter says that for a function between x= -2 and x=2, the average rate of change is 0.

the average rate of a change of a function between the points a and b is given by:

`(f(b)-f(a))/(b-a)`

for it to be equal to zero we have f(a)=f(b).

hence according to Hunter f(-2)=f(2).

Now maggie says that for the function between x= -2 and x=2 the graph goes up through a turning point and back down.

for both of them to be correct we can consider the example:

`f(x)=-x^2+4`