Please help me know the name of function:

y=(ax+b)^r

where "a", "b", and "r" are real constants and "r>0".

It is clear that for "r=1", this equation is general form of a linear function; and also for positive integer values of "r" (i.e. Natural numbers), this equation is a polynomial function. But I don't know whether there is a special function name for positive real values of "r" or not. Any reply is appreciated.