MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
The domain is the set of all "x" values and the range is set of all "y" values in a set of ordered pairs. Remember that ordered pairs are written as (x, y). When looking at a set of ordered pairs, find the domain by listing all the x values from the relation. Find the range by listing all the y values from the ordered pairs. Repeated values within the domain or range don't have to be listed more than once. In order for a relation to be a function, each x must correspond with only one y value. If an x value has more than one y-value associate with it -- for example, in the relation {(4, 1), (4,2)}, the x-value of 4 has a y-value of 1 and 2, so this set of ordered pairs is not a function. If each x-value corresponds with only one y-value, then the relation is a function.
When you're working with domain, range, relations and functions it's really important to keep all that vocabulary straight in your head. Keep in mind the domain is the set of all Xs, the range is the set of all Ys and in order to be a function each x has to have exactly one y.
So let's check out this problem. Find the domain and range, determine whether the relation is a function. Okay so the first thing I'm going to do is find the domain, the domain is the set of all x numbers. So when it's set up like this in ordered pairs you guys know the x numbers come first. So my domain is going to be 6, 4, 1 and 4 only I don't have to write that 4 twice. So it's going to be 6, 4 and 1 even though I have 4 points I only have 3 different values and I'm going to write them with these little curly brackets because again that's what we call set notation in Math. That's going to get more important as you go through your courses.
The range looks like this -1, 3 and 2. Again it's the y values -1, 3, 1 and 2. There we go I found my domain in range. That was the first part of the problem.
Next thing we have to do is determine whether the relation is a function and the relation would be a function if every x has exactly one y. So let's look 6 has -1, okay keep that in your head 4 goes with 3 okay, 1 goes with oh oh 4 goes with 3 there and 4 goes with 2 there? That's like two different y values for the same x. See that I have the same x number but I have different y values, that means this is not a function and the way I know again is because the x number of 4 is matched up with two different y values and in order to be a function each x only has to be exactly one y value.
So when you guys are asked to look at functions, find the domain and range and determine whether or not it's a function, just be really careful with the vocabulary, keep your notes out on x 2 if you can and that's going to help you keep straight what was the Xs again what's the Ys and is it the x that gets to pair whatever. Keep your notes out so it will help you a lot with this vocabulary stuff.
