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.

Tucker's statement that the average rate of change of the function between x=-3 and x=3 is 0 means that f(-3)=f(3). Karly's statement that the graph increases through a turning point and then back down can be consistent with Tucker's statement that the initial value is equal to the ending value, but with an increase and a decrease in the middle.