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.
The difference between Tucker and Karly's take is that Tucker's solution is analytical while Karly's is graphical. But both are correct either way.
For Tucker's solution, let's say at x=-3 the value for y is 4, and at x=3, the value of y is still 4, then the average rate of change or slope is 0. Note that the slope of the curve is Δy/Δx. Since there is no change for Δy, the slope is zero.
For Karly's solution, even if the curve travels high or low but would have the same elevation of x=-3 and x=3, the average rate of change is still zero. It is actually just same with Tucker's but Karly just verbalizes her solution that was observed visually.
