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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 2

Curriculum topic:  Maths and Numerical Reasoning

Curriculum subtopic:  Sequences

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

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

Find the function from the given inputs and outputs.

Input   Output
3
 
 
25
5
 
 
35
6
 
 
40
8
 
 
50

 

X → ________

x + 8 × 5

(x + 8) × 5

(x + 2) × 5

Find the function from the given inputs and outputs.

Input   Output
2
 
 
80
4
 
 
96
6
 
 
112
18
 
 
208

 

x → ________

x × 40

x + 78

(x + 8) × 8

Find the function from the given inputs and outputs.

Input   Output
3
 
 
3
5
 
 
7
7
 
 
11
19
 
 
35

 

x → ________

2x - 3

2 (x - 3)

2x - 6

Find the function from the given inputs and outputs.

Input   Output
3
 
 
-10
4
 
 
-5
5
 
 
0
11
 
 
30

 

x → ________

(x - 5) × 5

x - 5 × 5

x - 13

Find the function from the given inputs and outputs.

Input   Output
3
 
 
20
5
 
 
24
7
 
 
28
19
 
 
52

 

x → ________

x + 17

x + 7 × 2

(x + 7) × 2

Find the function from the given inputs and outputs.

Input   Output
1
 
 
-14
3
 
 
0
5
 
 
14
17
 
 
98

 

x → ________

x - 15

(x - 3) × 7

x - 21

Find the function from the given inputs and outputs.

Input   Output
4
 
 
-15
7
 
 
0
10
 
 
15
28
 
 
105

 

x → ________

(x - 7) × 5

x - 7 × 5

x - 19

Find the function from the given inputs and outputs.

Input   Output
1
 
 
-15
2
 
 
-12
3
 
 
-9
9
 
 
9

 

x → ________

x - 16

(x + 4) × -3

(x - 6) × 3

Find the function from the given inputs and outputs.

Input   Output
3
 
 
31
4
 
 
39
5
 
 
47
11
 
 
95

 

x → ________

8x + 7

10x + 1

12x - 5

Find the function from the given inputs and outputs.

Input   Output
3
 
 
10
7
 
 
18
11
 
 
26
35
 
 
74

 

x → ________

2x + 5

2x + 4

2x + 3

  • Question 1

Find the function from the given inputs and outputs.

Input   Output
3
 
 
25
5
 
 
35
6
 
 
40
8
 
 
50

 

X → ________

CORRECT ANSWER
(x + 2) × 5
  • Question 2

Find the function from the given inputs and outputs.

Input   Output
2
 
 
80
4
 
 
96
6
 
 
112
18
 
 
208

 

x → ________

CORRECT ANSWER
(x + 8) × 8
  • Question 3

Find the function from the given inputs and outputs.

Input   Output
3
 
 
3
5
 
 
7
7
 
 
11
19
 
 
35

 

x → ________

CORRECT ANSWER
2x - 3
  • Question 4

Find the function from the given inputs and outputs.

Input   Output
3
 
 
-10
4
 
 
-5
5
 
 
0
11
 
 
30

 

x → ________

CORRECT ANSWER
(x - 5) × 5
  • Question 5

Find the function from the given inputs and outputs.

Input   Output
3
 
 
20
5
 
 
24
7
 
 
28
19
 
 
52

 

x → ________

CORRECT ANSWER
(x + 7) × 2
  • Question 6

Find the function from the given inputs and outputs.

Input   Output
1
 
 
-14
3
 
 
0
5
 
 
14
17
 
 
98

 

x → ________

CORRECT ANSWER
(x - 3) × 7
  • Question 7

Find the function from the given inputs and outputs.

Input   Output
4
 
 
-15
7
 
 
0
10
 
 
15
28
 
 
105

 

x → ________

CORRECT ANSWER
(x - 7) × 5
  • Question 8

Find the function from the given inputs and outputs.

Input   Output
1
 
 
-15
2
 
 
-12
3
 
 
-9
9
 
 
9

 

x → ________

CORRECT ANSWER
(x - 6) × 3
  • Question 9

Find the function from the given inputs and outputs.

Input   Output
3
 
 
31
4
 
 
39
5
 
 
47
11
 
 
95

 

x → ________

CORRECT ANSWER
8x + 7
  • Question 10

Find the function from the given inputs and outputs.

Input   Output
3
 
 
10
7
 
 
18
11
 
 
26
35
 
 
74

 

x → ________

CORRECT ANSWER
2x + 4
---- OR ----

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