How to Find the Domain & Range of a Function

A detailed tutorial on finding the domain and range of a function. Step by step tutorial including several examples of how to find the domain and range of a function for reference.

Finding the domain and range is very important when given the graph of a function. The domain is the set of all possible x values of the function, and the range is the set of all possible y values of the function. When given a function, the first one you want to find is the domain. You want to figure out what is allowed for the x value. Typically, the domain ends up being the set of all real numbers, expressed a R. If the x is found in a fraction, it can be the set of all real numbers excluding 0. If the x is found in a square root, it is the set of all real positive numbers. It’s rare for there to only be a few values allowed for the domain. The next one you want to find is range. Very often, range also ends up being the set of all real numbers. But say you know that something has to come out negative, then it would only be the set of all negative numbers. Each function is a little bit different, but finding the domain and range is typically a very straightforward process.

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