What is great about this question is that you aren’t required to give numerical approximations of the rate of change over the interval. This means that you have a lot less work to do than you think.
Start by drawing a dot on each y-coordinate of every given x value in the interval table (-13, -10, -5, -2, and 0). Then, for each interval, draw a straight line between the two y-coordinates of the two x-values given in the interval. So, for interval A, you would draw a straight line from f(-13) to f(-10). This line would have a steep downward slope; this means that the average rate of change over this interval is negative, or less than zero. A satisfies the question.
Interval B has a positive slope between the two y-coordinates, so it doesn’t satisfy the question. Interval C has a line with a slope of 0, but does satisfy the question because it’s asking for average changes less than or equal to zero.
The answer for this problem would be intervals A and C, the answer that is selected.
