# 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
For example, the function is defined only if
For example, . Here,

*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.*x*â€“ 2 â‰¥ 0, or*x*â‰¥ 2. The two types of restrictions can be combined.*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*) =

*x*

^{2}is

*y*â‰¥ 0 since a square is never negative. The range of the function

*y*=

*f*(

*x*) =

*x*

^{2}+ 1 is

*y*â‰¥ 1 since

*x*

^{2}+ 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.