Select the correct answer.
what is the average rate of change of f(x), represented by the graph, over the interval [-2, 2]?

a. 8
b. 2
c. 1
d. 0
e. -1

Choice D) 0

Explanation:

The interval [-2,2] is the same as writing -2 <= x <= 2 where "<=" without quotes means "less than or equal to"

Focus on the lower bound of the interval (x = -2). If x = -2, then y = 4 giving us the point (-2,4) on this parabola. You can draw a vertical line through x = -2 on the x axis and you'll see this vertical line crossing the parabola at (-2,4)

Similarly, the point (2,4) also lies on the parabola. This time we use the x value x = 2 as this is the upper part of the interval.

So we'll use the two points (-2,4) and (2,4) to find the slope of the line through these points

m = (y2 - y1)/(x2 - x1)

m = (4 - 4)/(2 - (-2))

m = (4 - 4)/(2 + 2)

m = (0)/(4)

m = 0

The slope of this line is 0. Therefore the average rate of change on the interval [-2,2] is 0.

This is why the answer is choice D.

Side Note: the line that goes through the points (-2,4) and (2,4) is a completely flat horizontal line. All horizontal lines have slope 0.