Average Rate of Change

Question

What is the average rate of change of y with respect to x over the interval [-2,5] for the function y = 3x + 2

1) -9

2) 3

3) 1/3

4) -1

Answer 1

Here's another approach that may be a bit on the intuitive side if your are comfortable with recognizing graphs of various function types.

Since y = 3x + 2 is a linear function, you should know that all linear functions have a constant rate of change. The average rate of change is just as it sounds. It is the average change over the interval, in this case, the interval [2,5]. But if the rate of change or slope is constant, then its average is the same as the slope.

This means, the average rate of change = slope = 3

So the answer is #3

Now this way that I showed you is just thinking cleverly as if the original function was something other than a linear function, then the slope would not be constant and Tutor Jim J.'s method above would be the preferred method.

Answer 2

Hi Nick,

The average rate of change of a function over an interval is simply the slope of the line through the two points on the function. Since your interval of interest is [-2, 5], find the function value at -2 and at 5.

f(-2) = 3(-2) + 2 = -6 +2 = -4

The point (-2, -4) is on the function.

f(5) = 3(5) + 2 = 15 + 2 = 17

The point (5, 17) is on the function.

Find the slope of the line through these two points gives the average rate of change.

m = change in y / change in x

m = (-4 - 17)/(-2 -5)

m = -21 / -7

m = 3

Hope this helps! :)

JMJ