Some of the other mathematicians have got much better techniques for doing these but I resorted to trial and error and just looking for patterns.
I started by adding 3 to the y value because 0 to the power of anything is 0
x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | |
y | 159 | 29 | -1 | -3 | -1 | 29 | 159 | |
y+3 | 162 | 32 | 2 | 0 | 2 | 32 | 162 | 32=2^5 but 162 is not a power of 3 .. but 81 is |
(y+3)/2 | 81 | 16 | 1 | 0 | 1 | 16 | 81 | |
[(y+3)/2]^(1/4) | 3 | 2 | 1 | 0 | 1 | 2 | 3 | |
so .. working backwards
\(y=2x^4-3\)
I worked this out quite quickly because I have had a lot of practice but you should get a better answer off someone else