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

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`.