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General functions practice

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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Find the two requested rows. Subtract their outputs in the same order as their inputs, then divide. Round to the nearest hundredth when needed.

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US Letter

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Paper sizes and printing help · More general functions activities

Six tables. One or two intervals each.

Every worksheet contains six tables with six input-output pairs each. Choose six questions for one interval per table, or twelve questions for two intervals per table. Each calculation earns one mark.

Read the values directly from the table. The average rate is the change in f(x) divided by the change in x; it does not require guessing a formula for the function.

The answer key repeats each table and shows the substituted calculation, the exact result, and an approximate decimal when needed. Round halfway values away from zero: 0.125 becomes 0.13 and −0.125 becomes −0.13.

Learning objective

What this activity builds

Read two input-output pairs from a table and divide the change in output by the matching change in input.

Worked example

If f(−2) = 1.5 and f(4) = 6, what is the average rate?

(6 − 1.5) ÷ (4 − (−2)) = 4.5 ÷ 6 = 0.75.

The output increases by 4.5 as the input increases by 6. Dividing these changes gives 0.75 per input unit. Reversing both subtraction orders produces the same quotient.

Teaching notes

Make the practice count

  • Mark both requested rows before doing any arithmetic.
  • Keep the subtraction order the same in the numerator and denominator.
  • Use the two specified inputs, even when other rows appear between them.
  • Compare two intervals from the same table in the 12-question setting.
  • Keep exact values until the final step; round a halfway value away from zero.

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Math SheetNameScore/ 6TeacherDateAverage Rate of Change from TablesFind each average rate of change. Round to the nearest hundredth when needed; halfway values round away from zero.Table 1xf(x)-538.79-338.79038.79938.791138.791238.79Question 1: Rate from -5 to 9Table 2xf(x)-11-54.6-6-18.60-1.83-4.24-6.66-13.8Question 1: Rate from -6 to 0Table 3xf(x)-120.8-80.4-60.2-1-0.390.7121Question 1: Rate from -12 to 9Table 4xf(x)-8-0.44-7-0.411-0.172-0.145-0.0580.04Question 1: Rate from 2 to 8Table 5xf(x)-6-1.5-5-1.4-4-1.31-0.85-0.4100.1Question 1: Rate from 10 to 5Table 6xf(x)-12-17-2-0.1-1-0.061-0.173.141216.84Question 1: Rate from 7 to -12math-sheet.comPage 1 / 1

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