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Link Inputs and Outputs

In this worksheet, students will learn to understand functions as rules for linking inputs and outputs.

'Link Inputs and Outputs ' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Functions are rules that link inputs and outputs. In a function, each input has only one corresponding value of an output.

Here is an example of a function with a rule times by 2.

The picture below does not show a function, just a relationship between numbers. This is because 1 is linked with two outputs, and in functions, each input must have only one corresponding output.

 

Here are four representations of functions/relationships. Tick those which show functions.

 

A

B

C

D

The function links inputs and outputs with a rule &multiply; 2 then + 5.

What is the output, if the input is -2?

The function links inputs and outputs with a rule &multiply; 2 then + 5.

If the output is 9, what was the input?

What is the rule that links the inputs and outputs below?

Add 3

Subtract 3

Multiply by 3

Divide by 3

What is the rule linking inputs and outputs of the function below?

Add 3

Add 4

Subtract 4

Multiply by 3

Match functions below to the rules that link the inputs and the outputs.

 Add 5Subtract 5Multiply 7Divide 2
A
B
C
D

How many corresponding outputs can each of the inputs of a function be linked to?

1 only

2

7

infinite number

The function below is missing two outputs. What are they?

 Output 6Output 7Output 10Output 11
Input 3
Input 5

The function below is missing two inputs. What are they?

 Input 3Input 4Input 6Input 7
Output 13
Output 19

Match the inputs on the left with the outputs on the right for a function with a rule: multiply by 5, subtract 7.

Column A

Column B

3
8
6
3
2
28
7
23
  • Question 1

Here are four representations of functions/relationships. Tick those which show functions.

 

CORRECT ANSWER
A
D
EDDIE SAYS
Only A and D show functions. Each element of the inputs is linked to EXACTLY ONE element of the outputs. B is not a function because 11 is linked with both 3 and 4. C is not a function because 7 is not linked with any of the outputs.
  • Question 2

The function links inputs and outputs with a rule &multiply; 2 then + 5.

What is the output, if the input is -2?

CORRECT ANSWER
1
EDDIE SAYS
Start with -2. Multiply -2 by 2. You get -4. Now add 5 to -4. The answer is 1.
  • Question 3

The function links inputs and outputs with a rule &multiply; 2 then + 5.

If the output is 9, what was the input?

CORRECT ANSWER
2
EDDIE SAYS
To work out the input, you need to go backwards and use inverse operations. Instead of + 5, take 5 away. 9 - 5 = 4 Now instead of multiplying by 2, divide by 2. 4 ÷ 2=2 So the input was 2.
  • Question 4

What is the rule that links the inputs and outputs below?

CORRECT ANSWER
Multiply by 3
EDDIE SAYS
Did you remember to go from inputs to outputs. To get from 2 to 6 you need to multiply by 3, from 7 to 21 you also multiply by 3 so this is the rule of this function.
  • Question 5

What is the rule linking inputs and outputs of the function below?

CORRECT ANSWER
Add 4
EDDIE SAYS
Think about how to get from 3 to 7, 12 to 16 or 9 to 13. Have you noticed that it's always + 4?
  • Question 6

Match functions below to the rules that link the inputs and the outputs.

CORRECT ANSWER
 Add 5Subtract 5Multiply 7Divide 2
A
B
C
D
EDDIE SAYS
In A you always multiply by 7 to change the input into output ( 1 × 7 = 7, 5 &time;s 7 = 35). In B the rule is to subtract 5. The third function adds 5 to each input in order to generate the output. Finally, in D, each input is divided by 2 (8 %divide; 2 = 4, 24 ÷ 2 = 12).
  • Question 7

How many corresponding outputs can each of the inputs of a function be linked to?

CORRECT ANSWER
1 only
EDDIE SAYS
The definition of a function is that it links each input with ONE output.
  • Question 8

The function below is missing two outputs. What are they?

CORRECT ANSWER
 Output 6Output 7Output 10Output 11
Input 3
Input 5
EDDIE SAYS
Did you spot that each input is doubled first and then you add 1? The missing outputs are: 3 × 2 + 1 = 7; 5 × 2 + 1 = 11.
  • Question 9

The function below is missing two inputs. What are they?

CORRECT ANSWER
 Input 3Input 4Input 6Input 7
Output 13
Output 19
EDDIE SAYS
What's the rule here? It's multiply by 3 and then add 1. To work out the inputs, go backwards, first subtract 1 and then divide by 3. 13 - 1 = 12 12 ÷ 3 = 4 19 - 1 = 18 18 ÷ 3 = 6 The missing outputs are 4 (links with output 13) and 6 (links with output 19).
  • Question 10

Match the inputs on the left with the outputs on the right for a function with a rule: multiply by 5, subtract 7.

CORRECT ANSWER

Column A

Column B

3
8
6
23
2
3
7
28
EDDIE SAYS
Multiply each number of the left by 3 before subtracting 7 from that answer. 3 × 5 - 7 = 8 6 × 5 - 7 = 23 2 × 5 - 7 = 3 7 × 5 - 7 = 28
---- OR ----

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