INSTRUCTOR: In this video, we're finding domain and range when we're looking at some parabolas. So domain on this one-- remember, domain is our x values. So we're going to do is we're just going to have a set up kind of like start and stops that we had earlier. We're going to be looking low points and high points. 

Now, notice I ended this parabola so it doesn't continue to go on forever. It starts here, we're going around, and then it stops. So for x values, lowest value I have is here. Highest value I have is here. And of course, everywhere in between is included because we have curve in there. 

So our low point-- 1, 2, 3-- is at negative 3. Our high point-- 1, 2, 3-- is at positive 3. So we're going from negative 3 to 3. And if I wanted to, I could go ahead and label those points. Negative 3. 1, 2, 3, 4, 5, 6, 7, 8, 9. So that's negative 3, 9. And this one is at 1, 2, 3, 1, 2, 3, 4, 5, 6, 7, 8, 9. Positive 3, 9. And you'll see, those are my x values. 

If I had put my less than symbols in there, I know negative 3 is less than whatever x is, which is less than 3, which means everything is included between negative 3 and 3. And this endpoint has an open circle, so I'm not going to get an equal to. This endpoint also has an open circle, which means it's not included, so I do not get an equal to. 

Now, for the range, some people would be guessing that it was only 9, because it starts here, and it stops here. Remember, we're going down and then back up. And our range is supposed to be telling us lowest y value to highest y value. So our lowest y value is right here at the origin, and our highest y value is up here at 9. And of course, we're talking about all y values in between. 

So we start with our y. The lowest we said was 0. Highest we said was 9. So we're going from 0 to 9 for our range values. At the 0 end, we have a shaded in circle, so that means it is included in our answer. Up at the top where we have the nines, both of them have open circles, so it is not included, so I'm not going to put an equal to. 

Check out another example. Notice this one has an open circle down at the very bottom, or the vertex, but it continues on forever going upwards. Means it's also going to continue on going outwards. So if it's going to continue on in both directions for my x, I know it's going to continue to widen out this way. 

It's always going to widen out, which means I can count everything going to the left. Same thing going this way. This is going to continue to widen out. As it gets bigger, it's just going to widen and widen and widen and widen. And as it widens out, I'm going to continue to get all of the x values this way. 

So I'm going to be able to include all x values that way and all x values that way. The only thing I'm not going to be able to include is the x value right here because that's the one part not included. So I'm going to say that x cannot be equal to 1 2, 3. But x could be anything else. So x is typically all real numbers except positive 3. 

For our range values, I know it starts here, and it's going to continue to go up forever and ever and ever. So this is kind of a blend of some of the domain and ranges that we've looked at before. We're still looking low to high. The low looks like it's at negative 2, but the high goes on forever. 

So we're relating the y to that. So which is going to be bigger? All of these y values, or the negative 2? If I write it this way, then I would put that the y is greater than the negative 2. Some people would prefer to put that listing their y first, their negative 2. 

And they'd say all of the y values are going to be greater than negative 2. Are these two the same? They are. Notice at this point, there's an open circle, so I'm not going to add an equal to to those. But I could choose one of those two answers.