How do you determine the domain and range of relations and functions? - Answers

Some functions are only defined for certain values of the argument. For example, the the logarithm is defined for positive values. The inverse function is defined for all non-zero numbers. Sometimes the range determines the domain. If you are restricted to the real numbers, then the domain of the square root function must be the non-negative real numbers. In this way, there are definitional domains and ranges. You can then chose any subset of the definitional domain to be your domain, and the images of all the values in the domain will be the range.