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

The function value at -3 and 3 are equal and the function increases and then decreases only once.

Explanation:

According to Tucker , if average rate of change is 0 then f(-3) = f(3)

and according to Karly, the function first increases and then decreases til x = 3

So, if we try to solve their disputes with the help of a function, then we get a function whose initial and final positions are same and also there is only one time increase and decrease in the function between x = - 3 to x = 3

Answer 2

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.