Question

The set of ordered pairs represents a function. Write a rule that represents the function? (0,0), (1,5), (2, 40), (3, 135), (4, 320). Y=?

Answer 1

`y = 5x^3`

Explanation:

Firstly, we have to find a pattern. It does look like all values of `y_x` are multiples of `5` and of `x`, but what else ?

Since `y_x` is a multiple of `5` and a multiple of `x`, we can divide `y_x` by `5*x` to get :

`y_1/(5*1) = 1=1^2`

`y_2/(5*2) = 4=2^2`

`y_3/(5*3) = 9=3^2`

`y_4/(5*4) = 16=4^2`.

You can clearly see a pattern here ; `y_x/(5*x) = x^2`.

Therefore `color(red)(y = 5x^3`.