General functions
Average rate of change from tables worksheets
Find average rates from six function tables. Choose 6 or 12 questions, print Letter or A4, and check each result with a separate worked answer key.
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Average rate of change from graphs worksheets
Read four function graphs and estimate their average rates of change. Choose linear, quadratic, cubic, sine or exponential curves, with secants and worked answers.
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Locate the two requested inputs and read their outputs from the curve. Join the points with a straight secant, then divide the change in output by the change in input.
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Read the curve. Draw the secant.
Choose the curve for each of four questions independently: linear, quadratic, cubic, sine or exponential. Every graph has a unit grid from −10 to 10 on both axes, with room to draw a secant and write the average rate.
The student sheet gives two inputs without marking the points or revealing a formula. Read the outputs from the curve. The selected points lie on whole or half units so learners can check them against the grid.
The separate key marks both points with open circles, joins them with a blue secant and shows their coordinates and the substituted quotient. Reference values use exact endpoints and round to the nearest hundredth when needed. Allow reasonable graphical estimates when marking.
Learning objective
What this activity builds
Read two points from a function graph and use the slope of their secant to describe average change over an interval.
Worked example
A graph passes through (−2, 5) and (4, −1). What is its average rate on this interval?
(−1 − 5) ÷ (4 − (−2)) = −6 ÷ 6 = −1.
The secant goes down 6 units as it moves right 6 units. Its slope is −1, even if the curve rises or bends elsewhere between the points.
Teaching notes
Make the practice count
- Use one grid square per unit on both axes.
- Mark the requested inputs on the horizontal axis before reading the curve.
- Check for half-unit outputs between grid lines.
- Keep the subtraction order the same in the numerator and denominator.
- Round the final reference value to the nearest hundredth when needed; halfway values round away from zero.
- Allow reasonable reading estimates and ask learners to show their chosen points and secant.
- Compare a zero average rate with a curve that is not constant between its endpoints.
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