Skowhegan Area High School

Contemporary Mathematics In Context                                                                                      skowbutton msadbutton


Domain and Range

The domain of a function is the set of x values for your function, if your x values are the input.
The example that we'll use is the function y=20+1x.

There are two types of domains you can use, practical and theoretical.
The practical domain deals with numbers that are realistic in a problem situation. For example, if the function y=20+x represented a problem where y is the total pay for a babysitting job, the 20 represents $20 for just showing up, and the 1 means $1 per house for x number of hours. Now the practical domain would be between 0 and 10 hours, because that was the agreed job length.
While the practical domain values have been described above, the theoretical domain is the other type of domain. The theoretical domain is a set of logical numbers that would generate a reasonable output. The theoretical domain would therefore be all real numbers.

The range of a function is the set of y values for your function, if y is the output.

There are two types of range as well, practical and theoretical. The practical range for this function would be your pay for the 10 hours, which would be anywhere from $20 to $30.

The theoretical range again applies only to the function and would be all real numbers.
Some of these equations have limits on both domain and range. For example, in the function , the theoretical domain is all real numbers, but the range would be limited to all real numbers greater than or equal to negative 2. Other restrictions are specific to the functions, and most easily seen in the graph.