Average rate of change worksheet for Precalculus
The average rate of change is the slope between two points on the graph, so it is rise over run with the function doing the work. The difference quotient is the same thing with the second point written as h away from the first.
Also taught in Calculus, Algebra 2 and Algebra 1, each at its own level and with its own examples.
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Sigma Prep · sigmaprep.io/worksheets Name Average Rate of Change Date Period Find each rate of change, and answer what is asked. Leave answers exact.
Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep |
Sigma Prep · sigmaprep.io/worksheets Name Average Rate of ChangeAnswer keyVersion 1 Date Period Find each rate of change, and answer what is asked. Leave answers exact.
Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep |
How to do these
Average rate of change of on
- f(4) is 16 minus 12, which is 4.
- f(1) is 1 minus 3, which is -2.
- The rise is 6 and the run is 3.
The answer is .
Where students go wrong
Dividing by the wrong run, or subtracting the outputs in one order and the inputs in the other. Keep the same endpoint on top and bottom: f(b) minus f(a) over b minus a, in that order both times.
Also called average rate of change over an interval, difference quotient or slope of a secant line.
What you can put on this worksheet
- Average rate of change over an interval
- Average rate of change of on →
- The difference quotient
- Simplify for →
- The equation of the secant line
- Write the equation of the secant line of from to →
- The general difference quotient
- Simplify for →
- From a table
- Find the average rate of change from to . →
- Are the rates increasing or decreasing?
- Find the average rate of change over each interval. Are the rates increasing,
decreasing or the same, and what does that show?
→ ; the same, so the graph is a line - Average speed and the speed limit
- A car passes mile marker 32, and 30 minutes later it passes mile marker 67. The speed limit is 55 mph. Must it have gone faster than the limit at some moment? → Average speed mph; yes: by the mean value theorem it went exactly 70 mph at some moment
- From a graph, fractional endpoints
- The graph of is shown. Find its average rate of change on →