Question

A function is graphed below. On which

interval of x is the average rate of change
of the function the smallest?
X
3
7
21
39
65
Y
3
18
28
36
40

Answer 1

The x-axis interval of 39 to 65 has the smallest rate of change.

Explanation:

See the attached worksheet. The interval of x that results in the least change in y can be visually seen by plotting the points and drawing a curve. The curve begins to flatten as x increases. So the smallest rate of change is between the last two points, x = 39 to 65.

This can also be calculated by finding the change in y per a change in x. The table in the graph confirms the earlier observation. Dx and Dy represent the "delta," or difference, D, between the x (Dx) and y(Dy) values. The rate of change is calculated as Dy/Dx, or the change in y divided by the change in x. The results confirm that the 39 to 65 segment is the smallest, at 0.15.