1. 3.4 Average Rate of Change
Average Rate of Change (A.R.O.C.): change in the function values over the change in the input values.
For a function, y = f(x), between x = a and x = b, the A.R.O.C is:

2. Example 1
Find the average rate of change between the indicated points.
A.R.O.C. = y
(-16, 6) 9 3 x
-16
-12 -8 -4 4 8 12 16
(-4, -6) -9

3. Example 2
Find the average rate of change between the indicated points.
A.R.O.C. = y
(-16, 6)
(12, 9) 9 3 x
-16
-12 -8 -4 4 8 12 16 -9

4. Example 3 Find the average rate of change of the function between
the values of the variable.
A.R.O.C.

5. Example 4 Find the average rate of change of the function between
the values of the variable.
A.R.O.C.

6. Example 5
A man is running around a track 200 m in circumference. With the use of a stopwatch, his time is recorded at the
end of each lap, seen in the table below.
What was the man’s speed between 66s and 209s? Round answer to the nearest hundredth.
Time (s)
Distance (m) 32
200 66
400
104
600
153
800
209
1000
270
1200
341
1400
419
1600
Calculate the man’s speed for each lap.
Please round answer to the nearest hundredth.