According to Wikipedia:
In mathematics, a parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. For example, for the family of quadratic functions having the general form

the simplest function is
.
So here the parent function is just y = log(x), I guess. If we restrict ourselves to real numbers only, then the domain is x>0 and the range is -infinity to infinity.
Hiowever, the term "parent function" isn't one in general use in mathematics as far as I'm aware. I suspect it's just used in education for some purposes.
According to Wikipedia:
In mathematics, a parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. For example, for the family of quadratic functions having the general form

the simplest function is
.
So here the parent function is just y = log(x), I guess. If we restrict ourselves to real numbers only, then the domain is x>0 and the range is -infinity to infinity.
Hiowever, the term "parent function" isn't one in general use in mathematics as far as I'm aware. I suspect it's just used in education for some purposes.