Question

Two students in your class, Ralph and Bobby, are disputing a function. Ralph says that for the function, between x = −1 and x = 1, the average rate of change is 0. Bobby says that for the function, between x = −1 and x = 1, the graph goes up through a turning point, and then back down. EXPLAIN how Ralph and Bobby can both be correct, using complete sentences.

Answer 1

Ralph and Bobby both are correct about slope. Because slope for both is 0.

Explanation:

We are given a function that has two values of x's between x = −1 and x = 1.

And the average rate of change between x=-1 and x=1 is 0.

We know that x=-1 and x=1 are the points on x-axis.

If we joint x=-1 and x=1 points, we would get a straight line horizontal line on x-axis.

And note, the slope of a horizontal line is 0 always.

So, according to Bobby the graph goes up through a turning point, and then back down that means the point (-1,0) gets horizontally shift by 2 unit at (1,0).

Therefore, rise/run = 0/2, that is also equal to 0.

Therefore, Ralph and Bobby both are correct about slope.

Because slope for both is 0.