[Music] let's get the domain and range from a graph I laugh at these three examples but in order to do that we need to get a definition relation is any set of ordered pairs the set of all first components of the ordered pairs is called The Domain the set of all second components is called the range okay now that we have that definition we know a little bit more about the domain in the range whoa this example here yeah um the domain is the set of all X values so I want to see which X values are being represented yeah all right this one's in there and this one's in there and this one's in there and this one's in there and this one's in there and this one's in there and this one's in there but that one there it's not there so the domain goes from what appears to be a minus three all the way to 1 2 3 4 in the positive now that's a closed dot so that is represented and I'll represent it like that but this side is an open Dot so it's represented by open and you're left with that clopin interval half open half close and then I ran down here to the range she like the boy with the big old chain around town in the big old range okay it's not that one you didn't like that how'd you like that okay so then the range is the set of all y values and that's why my range go from a minus 2 to one because when I'm looking at the range I'm looking at uh this stuff this stuff this stuff and stop cuz it's a set of all y values and that's why I go from - 2 two one Fun open on this side closed on that side now iide with this example over here okay you ready the domain is the set of all X values oh which X is are represented oh you're here you're here you're here you're here you're here you're here it's like roll call and this one continues to go in continue just it doesn't stop it just continues to go so all of the X values are represented and that's how I represent my domain from minus infinity all the way up to a positive infinity and beyond let's buzz on down to the range sure the range is the set of all y values is this y value represented by that blue graph no this one no this one no yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes our range is restricted to everything above two so then we do go from two to infinity and beyond do I include the two sure because it's included in the range now I Ponder and I wonder does the order matter yes this is interval notation lowest leftest highest rightest now I might as do this one yeah here it looks like here it looks like all my xes they're in no they're represented so my domain is minus infinity all the way up to infinity and my range all my y values are also listed so that one's minus infinity up to positive infinity and then uh Rockstar [Music]