
Classifying functions
y = 4t^6 + t^4  pi
Is this only a polynomial function and algebraic function?
y=x^9
Is this only a power function?
There are a few more choices:
Power function
Root function
Rational function
Trigonometric function
Exponential function
Logarithmic function

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).