By the end of this resource, you will be able to identify domain and range from any given contextual situation.

Determining the domain and range from a linear or quadratic contextual situation is similar to determining the independent and dependent variables.

Let's first look an example:

Suppose you are interviewing for a job. Your employer offers you the choice of two different options for your pay. The first option is to pay you \$10.00 per hour and give you a raise of \$.50 per hour at the end of the year. The second option is to pay you \$11.50 per hour and give you a raise of \$.25 per hour at the end of the year.

First, find a function for each option. To do that, you have to know what the domain and range might be. Let y = the amount you will make at the end of the year and x = the number of hours you work. Thinking about what would be reasonable values for x and y will help determine the domain and range.

First, let's think about the domain. Since x represents the numbers of hours you worked for the year, would it be reasonable to have negative values? If you said NO, you would be correct. We can assume the lowest possible value in the domain would equal zero. So, our domain would be {x| x ≥ 0}.

Now, let’s think about the range. Since y represents your earnings at the end of the year, would it be reasonable to have negative values? If you said NO again, you would be correct. You cannot earn a negative amount. We can assume the lowest possible value in the range would also equal zero. So, our range would be {y | y ≥ 0}. You should be able to relate with this situation since you may have to make a decision in comparing two or more job offers in your future.

It's important to realize that every situation is different and you must think about what is reasonable.