Two students in your class, Hunter and Maggie, are disputing a function. Hunter

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. 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.

Explanation / Answer

if we take a function

f(x) = (x-2)(x+2)(x-5)

avearge rate of change from x = -2 and x = 2 is

f(2) = (2-2)(2+2)(2-5) = 0

f(-2) = (-2-2)(-2+2)(-2-5)= 0

so, f(2) - f(-2) / 2 +2 = 0

and the graph goes up through a turning point and then goes down from x = -2 to x = 2

so, both can be correct

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