### Finding domain and range — with color!

Have you ever noticed that a lot of students struggle with the idea of domain and range? This concept, taught mostly in Algebra 2, often confuses students to the point where they cannot even identify the domain and range of a simple, continuous function.

I don’t really understand why students struggle with this concept, but I recently found a way of showing the idea that makes it considerably easier — using color to mark up a function.

Here’s an example of a problem where students need to figure out the domain and range by looking at a graph, like this:

What I have students do is use two colors to sort of “box in” the function. With one color, green in this case, students mark the left bound and right bound of the function by drawing vertical lines. And with another color, red, students mark the lower bound and upper bound by drawing horizontal lines. I have students write in the phrases: left bound, right bound, lower bound, and upper bound, like this:

Finally I ask students to figure out the domain and range by writing three-part inequalities for x and y, respectively, like this:

I’ve used this approach with a number of students, and so far no one has been unable to find the domain and range when using it. So it appears to be a winner. Try it yourself, either as you teach a concept, or as you re-teach it to those who are struggling.