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

@mathmate

Answer 2

To answer this question, you need to know the meaning of the words.
If you don't already know them, here're some links that can help you:
average rate of change between a and b (b>a)
= (change in y)/(change in x) = \(\Large \frac{f(b)-f(a)}{b-a}\)
(see also
http://cims.nyu.edu/~kiryl/Precalculus/Section_2.4-Average%20Rate%20of%20Change/Average%20Rate%20of%20Change.pdf
)
and for turning point, look under "turning point" in
https://www.mathsisfun.com/algebra/polynomials-behave.html

Now you can try to sketch a graph between -3 and +3 that satisfies the description given in the question, and explain accordingly.