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Find the Function from the Given Inputs and Outputs

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

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

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Translate Situations/Procedures into Expressions, Formulae and Graphs

Difficulty level:  

Worksheet Overview

In this worksheet, you must find the function which 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 which took 3 to 25, 5 to 35 etc.


This demands some detective work, but looking at the outputs, we see that they are all multiples of 5.


This suggests that the second operation was ×5.


Now go backwards:


25÷5 = 5
35÷5 = 7
40÷5 = 8
50÷5 = 10


Notice that these are all 2 more than input.


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

 

Answer:

(x+2) × 5

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