Precal

Any specific kind of function, or just functions in general? The specific formulas depend on the specific function you're talking about.

Domains


Domains are fairly straight forward. Ranges are more fun. Typically, the domain is going to be of the form...

"All {Real} numbers {<,>,ne} restriction."

Where the values in brackets might be substituted with other values. Example:

y = 1/x

The domain is "all real numbers not equal to zero". Obviously, x=0 is not defined.

y = 1/(x^2-1) All real numbers not equal to 1 or -1.
y = sqrt(x) All real numbers >= 0

For parabolic equations, you can use the discriminant theorem to find solve the equation sqrt(b^2-4a(c-m))=0 where m is either the minimum or the maximum of the equation. Correct me if i'm wrong, because I've never been formally taught that in school, I was just really bored during class one day.