Interval notation, as you may know, is just listing the intervals over which a function is defined. For example, if you see

Range:

that means that the range of the function is all the values from -1 to 3, including -1 but not including 3. (The bracket means including; the parenthesis means not including.) A lot of functions have domains or ranges which extend all the way from negative infinity to infinity. This is written

Domain:

which means that x can take on any value, all the way from negative infinity (that means any negative number) up to positive infinity (zero and any positive number). Notice that we use parentheses when dealing with infinity, which means that x can take on any value up to,but not including, infinity. That's because infinity is not a real number; it's just a shorthand for an idea - no number can actually "equal" infinity.

Set builder notation is just a little different. Instead of dealing with intervals, it usually deals with inequalities or other conditions. So to write "the domain of f(x) is all numbers such that x is not equal to zero and x is not equal to 4" in set builder notation is

A breakdown of this notation is

means "all x"

means "such that"

means "x"

means "is not equal to"

means "0"

means "and"

means "x"

means "is not equal to"

means "4"

A verbal description, which is probably your best bet if you don't have a lot of time to learn this stuff in one night, is simply describing the domain or range in words like I did above. However, this can get inelegant with more complicated functions. Example:

"The domain of f(x) is all numbers below or equal to three, and all numbers above four."

Here's a breakdown of the three methods, using the domain "all real numbers" - ie, the case in which the function can take on any value for x.

Interval notation:

Set builder notation:

Verbal description: "All real numbers"