There is a formal definition of a function, but it's much easier to use something called the vertical line test. If you graph your expression and you can always make a vertical line that only touches one point, it's a function.
Put another way, given any value of x, there must only be one f(x) or y that goes along with it. If there is there is more than one (like having the points (2,1) and (2,5) ) then it's not a function.
is only the top half of a side ways parabola. It's a function. But if you include the other half it isn't a function.
The best way to get a sense of this is to be familiar with lots of graphs and how they are formed. A lot of terms and exponents will generally be less likely to be a function.