For the function f(x) = 2|x – 1|, what is the average rate of change over the interval –1 ≤ x ≤ 1?

Question

Can someone please explain how to find the average rate of change? I totally forgot!

Answer 1

Average rate of change equates to "What is the slope?" in mathematics, or at least in this question.

2|x-1| is just a "V" Shape that is has been shifted to the right by 1 away from the origin.

The slope is simply the number in front. However, is it positive or negative rate of change?

To do this we must look at the graph (I suggest typing it into Desmos.com if you do not know what the graph looks like).

And as you can see, from -1 all the way to +1 on the "X" axis our graph is going down as we move left to right.

Therefore the answer is -2 units.

Answer 2

It's an absolute value of 2*|x| that shifted to the right by 1.

The slope will be -2 as it is decreasing on the left side.