Domain and Range
The domain of any equation is the set of all x's which we can plug in the equation & get back a real number for y. The range of any equation is the set of all y's which we can ever get out of the equation.
Note that we did mean to employ equation in the definitions above rather than functions. These are actually definitions for equations. Though, as functions are also equations we can employ the definitions for functions as well.
Finding the range of an equation/function can be pretty hard to do for various functions and thus we aren't going to actually get into that. Here we are much more interested in finding the domains of functions. From definition the domain is the set of all x's which we can plug in a function & get back a real number. At this instance, that means that we have to ignore division by zero and taking square roots of negative numbers.