In this activity, we will be finding the function that turns all the inputs into their outputs.

Example:

We want to find the two operations that took 3 to 25, 5 to 35 etc.

This demands some detective work!

Looking at the outputs, we see that they are all multiples of 5.

This suggests that the second operation was x5

Now go backwards:

25 ÷ 5 = 5
35 ÷ 5 = 7
40 ÷ 5 = 8
50 ÷ 5 = 10

Notice that these are all 2 more than the input.

The function is therefore  x → (x + 2) × 5

Answer:

(x + 2) × 5

Are you ready to have a go at some questions now?