Function machines

A function machine is a way of writing rules using a flow diagram.

The equation \(3j - 6 = 9\) can be shown on a function machine by writing out the functions that have been applied to \(j\) in the order they happened. BIDMAS means multiplication happens before subtraction.

\(3j - 6 = 9\) means \(j\) has been multiplied by 3 and then 6 has been subtracted. The answer is 9.

On a function machine, this would look like this.

Example

Create a function machine for the equation \(6j + 7 = 43\).

\(6j\) means \(6 \times j\), so \(j\) has been multiplied by 6. Then 7 has been added. The answer is 43.

Begin with the letter \(j\), and then show in order what functions have been applied to the letter.

Using function machines to solve equations

Function machines can be used to solve equations by reversing, or finding the of the steps.

Example

Solve the equation \(3j - 6 = 9\) using a function machine.

Firstly, write the equation as a function machine.

Then, find the inverse of each step. This means turning multiplications into divisions and subtractions into additions. Also, instead of starting at the beginning of the function machine, now start at the end.

Now follow the function machine in reverse:

\(9 + 6 = 15\)

\(15 \div 3 = 5\)

So: \(j = 5\)

Check this answer by substituting \(j = 5\) into the original equation:

\(3j - 6 = 9\)

\(3 \times 5 - 6 = 9\)

\(15 - 6 = 9\)

\(9 = 9\)

The equation balances, so \(j = 5\) is the correct answer.

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Solving linear equations - EdexcelFunction machines