# what is the function rule for (1,2), (2,16), (3,54), (4,128), (5,250)?

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To find the function rule, it is important to find any invariant values for each x-value. In this case, we see that if we cube each x-value and then multiply by 2, we get the corresponding y-value. That is:

`2times (1)^3=2`

`2 times(2)^3=2(8)=16`

`2times(3)^3=2(27)=54`

`2times(4)^3=2(64)=128`

`2times(5)^3=2(125)=250`

**This means the function rule is `y=2x^3` .**

This is a power regression, with the equation y=2x^3.

You can plot this on a graphing calculator to solve, which is the easiest solution. However, to do it with algebra, you need to have a mental picture of what the graph looks like to determine what type of equation to use. Afterwards, plug in numbers to try to make a fit.