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Find the Function from the Given Inputs and Outputs

In this worksheet, students will find functions from the given inputs and outputs.

'Find the Function from the Given Inputs and Outputs' worksheet

Key stage:  KS 2

Year:  Year 5 11+ worksheets

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Sequences

Difficulty level:  

Worksheet Overview

In this activity, we will be finding the function that turns all the inputs into their outputs.



Input   Output


We want to find the two operations that took 3 to 25, 5 to 35 etc.

This demands some detective work!


detective with a magnifying glass


Looking at the outputs, we see that they are all multiples of 5.

This suggests that the second operation was x5

Now go backwards:

25 ÷ 5 = 5
35 ÷ 5 = 7
40 ÷ 5 = 8
50 ÷ 5 = 10

Notice that these are all 2 more than the input.

The function is therefore  x → (x + 2) × 5



(x + 2) × 5


Are you ready to have a go at some questions now?


carrot thumbs up


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