# Find the Function from the Given Inputs and Outputs

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

Key stage:  KS 3

Curriculum topic:   Algebra

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

Difficulty level:

### 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

(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 → ________

(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 → ________

(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 → ________

2x - 3
• Question 4

Find the function from the given inputs and outputs.

Input   Output
3 -10
4 -5
5 0
11 30

x → ________

(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 → ________

(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 → ________

(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 → ________

(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 → ________

(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 → ________

8x + 7
• Question 10

Find the function from the given inputs and outputs.

Input   Output
3 10
7 18
11 26
35 74

x → ________

2x + 4
---- OR ----

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