Question

Which is the correct answer?

Answer 1

Answer:

D.

Step-by-step explanation:

The average rate of change of the function f is more than the average rate of change of x.

Here is why.

Look at the rates of change going from x = 0 to x = 3.

From x=0 to x=1, where x changes one unit, the value of f(x) only changes one-half unit, which is less than the change in x. But as you move to the right, see how the change in f(x) keeps getting larger and larger in magnitude? (Don't worry about the (-) sign.)

So, the average change in f will definitely be bigger than the average change in x, over the long run.

Now, look from x =0 and go back the other way, as x decreases 1 unit at at time. It is the same story.

If you would like to see this for yourself, look at the attached graphic.

Hope this helps.