  # Find the Function from the Given Inputs and Outputs

In this worksheet, students will find functions from the given inputs and outputs. Key stage:  KS 2

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.

Example:

Input   Output
3 25
5 35
6 40
8 50

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

This demands some detective work! 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

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