Question

Write the equation for the following relation. Include all of your work in your final answer.

\[Q=\left\{(x,y):(2,8),\ (3,27),\ (4,64),\ (5,125),\ ...\right\}\]

Answer 1

Given:

The relation is

`Q=\{(x,y):(2,8),(3,27),(4,27),(5,125),...\}`

To find:

The equation for the given relation.

Solution:

(2,8) is an ordered pair of given relation. So, y=8 at x=2.

`8=2* 2* 2`

`8=2^3`

Similar,

`27=3^3`

`64=4^3`

`125=5^3`

It means, y-values are cube of x-values. So,

`y=x^3`

Therefore, the required equation for the relation is
`y=x^3`.