Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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An important part of understanding functions is understanding their domain and range. **Domain and range** are all the possible x-values and y-values of the function, and can often be described easily by looking at a graph. In order to grasp domain and range, students must understand how to determine if a relation is a function and interpreting graphs.

So, we're now going to talk about finding the domain in the range of functions. And these are just two different terms in order to talk about different aspects of a relationship or a function. Okay, so domain is what we going to be the possible x values of a function. And the range is just the same thing but with the y values. Okay, the easiest way I have to remember this is they actually come alphabetically, so d comes before r, x comes before y. So when you're thinking about domain, x comes first, thinking about range, y comes second. So there's that sort of alphabetical representation that helps me remember it. If you have another way or if you just have memory, go ahead and remember the way you can.

Let's take an example, okay. So here we have, set f. Set of three different points, okay? And we're asked to find the domain. So domain is going to be a set of numbers, okay? And the domain corresponds to the x values. So here we have the x value, 1 from this point 3 from this point and 5 from this point. So put those together and that makes our domain. 1, 3 and 5. Through the same idea for the range, except range is going to correspond to the y values. So we look at the y values and we get which y values are represented 2, 4 and 6.

Now, just an easy way to talk about different aspects of a relationship. Domain is the x values, y is, the range is the y values.