# Domain and Range

We usually identify a function with its correspondence, as in the example above. However, a function consists of three parts: a domain, a range, and correspondence between them.

The domain of a function is the set of x values for which the function is defined.

For example, the function  is defined for all values of x â‰  1, which causes division by zero. There is an infinite variety of functions with restricted domains, but only two types of restricted domains appear on the SAT: division by zero and even roots of negative numbers.

For example, the function  is defined only if x â€“ 2 â‰¥ 0, or x â‰¥ 2. The two types of restrictions can be combined.

For example, . Here, x â€“ 2 â‰¥ 0 since itâ€™s under the square root symbol. Further x â€“ 2 â‰  0, or x â‰  2, because that would cause division by zero. Hence, the domain is all x > 2.

The range of a function is the set of y values that are assigned to the x values in the domain.

For example, the range of the function y = f(x) = x2 is y â‰¥ 0 since a square is never negative. The range of the function y = f(x) = x2 + 1 is y â‰¥ 1 since x2 + 1 â‰¥ 1. You can always calculate the range of a function algebraically, but it is usually better to graph the function and read off its range from the y values of the graph.