The domain is the set of all first elements of ordered pairs ( x -coordinates). The range is the set of all second elements of ordered pairs ( y -coordinates). Domain and range can be seen clearly from a graph.
SparkNotes: Algebra II: Functions: Domain
Therefore 1 is not in the domain of this function. All other real numbers are valid inputs, so the domain is all real numbers except for x1. What other kinds of functions have domains that aren't all real numbers? When working with functions, we frequently come across two terms: domain range. What is a domain? What is a range? Why are they important? Definition, domain : The domain of a function is the set of all possible input values (often the "x" variable which produce a valid output from a particular function. There's one notable exception: yconstant. When you have a function where y equals a constant (like y3 your graph is a horizontal line. In that case, the range is just that one value. The range of a simple linear function is almost always going to be all real numbers. A graph of a line, such as the one shown below on the left, will extend forever in either y direction. That's why the graph extends forever in the x directions (left and right). What kind of functions don't have a domain of all real numbers? Well, if the domain is the set of all real numbers for which the function is defined, then logically we're looking for a function that has certain input values that do not produce a valid. The domain of inverse sine is -1 to 1. However, the most common reason for limited domains is probably the divide by zero issue. When finding the domain of a function, first look for any values that cause you to divide by zero.