y = 4t^6 + t^4 - pi
Is this only a polynomial function and algebraic function?
Is this only a power function?
There are a few more choices:
Remember that some of these are subsets of the others. If by "power function", you mean something like [itex]ax^n[/itex], then all "power functions" are polynomials. And all polynomials are rational functions (in the same way that all integers are rational numbers).