![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 class=](https://us-static.z-dn.net/files/df1/478f75e16be8b179316002ee8b4bca13.jpg)
Answer: Choice D) 0
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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.
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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.