Question

Write an equation to represent the table:

x y
2 4
3 8
4 16

f(x) =

Answer 1

f(x) = 2^x
(The ‘^’ means ‘to the power of’)

To find this function, you first need to notice that the y values are powers of 2, and you can tell because they are doubling each time x increases: 4 × 2 = 8, 8 × 2 = 16, etc.

Once you’ve noticed that they are powers of 2, you then need to find out which powers of 2 they are. The first y value is 4 which equals 2², and the second y value is 8 which equals 2³.

This means that the power is the x value, so you end up with f(x) = 2^x

I hope this helps!