Question

Two students in your class, Hunter and Maggie, are disputing a function. Hunter says that for the function, between x = -2 and x = 2, the average rate of change is 0. Maggie says that for the function, between x = -2 and x = 2, the graph goes up through a turning point, and then back down. Explain how Hunter and Maggie can both be correct, using complete sentences.

Answer 1

@whpalmer4

Answer 2

The average rate of change between two points on the graph of a function is just the slope of the line that passes through those two points. It doesn't place any restrictions on what the function does between those two points, so long as it eventually passes through them.

The following all have the same average rate of change: