Question

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

Average rate of change will be given by: \[
\frac{f(3)-f(-3)}{3-(-3)} = \frac{f(3)-f(-3)}{6}
\]

Answer 2

For it to be \(0\), we need \(f(3)=f(-3)\).

Answer 3

However, this doesn't mean that \(f(0)=f(3)\), for example. All the points in between \(-3\) and \(3\) could be just about anything.

Answer 4

i dont understand what average rate of change really is or how they both could be correct