Question

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

Q = {(x, y): (2, 8), (3, 27), (4, 64), (5, 125), . . .}

Answer 1

`y=x^3`

Explanation:

The given relation is Q = {(x, y): (2, 8), (3, 27), (4, 64), (5, 125), . . .}

We can quickly recognize a pattern to write the equation of the given relation.

We can observe the following pattern among the x and y coordintaes.

`8=2^3`

`27=3^3`

`64=4^3`

`125=5^3`

We can see that the base of the powers on the right are the x-values of the relation and the values on the left are the y-values.

Hence, for any ordered pair (x,y), the equation is

`y=x^3`