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

Answer:below

Explanation:

Well, when you use the formula to find the rate of change, which is (y2-y1)/(x2-x1), so long as the 2 y-values are the same, it will result in 0/(x2-x1). So, regardless of what is in the denominator, the answer will always result in 0.

Answer 2

This can occur through a parabola that has zeroes at x = 3 and x = -3. There is no rate of change because the y values do not change at those points because they are both 0. Karly can be correct because that turning point can be a vertex of a parabola. The parabola's function would increase until it reaches it's highest point and then go back down again. In this way, Karly and Tucker can both be correct.

Hope this helps :)