Question

the point (-2,-32) is on the graph of an odd power function. What other point must be on this graph? write an equation for this function.

Answer 1

eq tor the function is \[f(x) = x ^{5}\]
to find other points on this graph, simply substitute x in the equation with any number

Answer 2

and if you are curious how to find the equation for any simple power function, simply use logarithms.
Ask yourself, to what power do I have to raise x to get y? In logarithmic form this question would be \[\log_{x} y = power\]
In your case it would be \[\log_{-2}-32 = 5\] hence you know that to get y you raise x to the 5th power, so the function will be \[f(x) = x ^{5}\] which you can also write as \[y = x ^{5}\]
NOTE that this method ONLY works for SIMPLE power functions