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

This function is a quadratic one and the graph is a parabola. Between (x = -3) and (x = +3) there is a max., and the axis of symmetry is at x = 0.
Tucker: f(-3) - f(3) = 0. Between x = -3 and x =3, the average change is zero. He is correct
Karly: The graph is a parabola goes up, reaches the max, then goes down, back to the same value. He is also correct.