Question

PLEASE HELP. Two students in your class, Tucker and Karly, are disputing a function. Tucker says that for the function, between x = -3 and x = 3, the average rate of change is 0. Karly says that for the function, between x = -3 and x = 3, the graph goes up through a turning point, and then back down. Explain how Tucker and Karly can both be correct, using complete sentences.

Answer 1

For the average rate of change to be zero from (-3 to 3) the function just has to have the same value at 3 and -3. What it does in between is irrelevant.

Answer 2

so if it symmetrical then it is correct?

Answer 3

Correct. A good simple example here is something like a parabola



the parabola can also open upwards as well