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.

$8=2\times 2\times 2$

$8=2^3$

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 $y=x^3$.