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Here is a function machine - OCR - GCSE Maths - Question 6 - 2019 - Paper 2

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Here is a function machine. (a) (i) Find the output when the input is 7. (ii) Find the input when the output is 42. (b) The input is x and the output is y. Wr... show full transcript

Worked Solution & Example Answer:Here is a function machine - OCR - GCSE Maths - Question 6 - 2019 - Paper 2

Step 1

Find the output when the input is 7.

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Answer

To find the output when the input is 7, we apply the operations of the function machine:

  1. Multiply the input by 5:

    7×5=357 \times 5 = 35

  2. Subtract 3 from the result:

    35−3=3235 - 3 = 32

Thus, the output when the input is 7 is 32.

Step 2

Find the input when the output is 42.

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Answer

To find the input when the output is 42, we need to reverse the operations of the function machine:

  1. Add 3 to the output:

    42+3=4542 + 3 = 45

  2. Divide the result by 5 to find the input:

    455=9\frac{45}{5} = 9

Thus, the input when the output is 42 is 9.

Step 3

Write an equation for y in terms of x.

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Answer

Given that the input is x and the output is y, we can set up the following equation based on the function machine's operations:

  1. The input x is multiplied by 5:

    5x5x

  2. Then we subtract 3 from that result to find y:

    y=5x−3y = 5x - 3

Thus, the equation relating y to x is y = 5x - 3.

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