Functions: inputs, output and tracing

Step 1 Warm-up recall

From M6.L1: name two parts of the receipt task.

Your answer

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Step 2 Learning goal

By the end of this lesson you can:

• define a function, input and output (Foundation);
• trace a call by hand (Core);
• write a short function from a description (Core).

Step 3 A familiar example

A calculator key such as the square root takes a number, gives back a number and hides the working. A function in a program does the same job for any step you name.

Step 4 Clear explanation

A function is a named part that takes inputs (also called arguments or parameters), does its work and gives back an output (the returned value). Using a function is a call. Here is an invented function: average(a, b) returns (a + b) ÷ 2.

To trace a call, replace the inputs by their values, do the working in order and write down the output. A function can be called many times with different inputs, so the working is written once and reused. A function should depend only on its inputs, so the same inputs always give the same output, which is what makes it easy to test. In a programming language, the rules for naming and calling functions differ in detail, but the idea is the same.

Step 5 Worked example (4 marks)

Trace average(6, 11) using average(a, b) = (a + b) ÷ 2.

1. Replace the inputs: (6 + 11) ÷ 2. (1 mark)
2. Add: 17 ÷ 2. (1 mark)
3. Divide: 8.5. (1 mark)
4. Answer: 8.5. (1 mark)

Step 6 Learner practice (instant-marked)

Step 7 Recap

• A function has inputs, working and an output.
• Trace a call by replacing inputs with values.
• The same inputs should give the same output.

Step 8 Exit ticket (ungraded)

Trace average(5, 9) and average(0, 7).

Your answer

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Step 9 Go further (Extension)

Write a function double(x) that returns x × 2 and trace it for 6 and 0.