Domain and Range - Problem 4

When you're asked to find domain and range of a graph that's continuous, like this, sometimes it can be kind of tricky. So what I really want you guys to try think about is that the x axis is the horizontal and the y axis is the vertical. Domain is the x numbers, so let's look at this graph and try to figure out what x numbers are possible for the curve that we're given.

So let's see if I were to look at my x numbers, the first place where an x value shows up in this graph is right here at three and I know that because the point is labelled for me. My x number could be three or it could be anything bigger than three, it could go on and on and on in the positive direction. So when I write this I'm going to write my domain as x numbers but x has to be bigger than or equal to 3. What that tells me is that x could be three, could be four, could be five could be six or seven, could be like infinity and the way that shows up in the graph is with this arrow.

This graph doesn't stop right there, it continues going off and off and off forever in that direction. So my x numbers, my domain can also continue in that direction. The range is the y values. So lets look at the y values y is up and down, my first y number that I hit is right there at one and then my y numbers go up from there. This graph is going out to the right forever and it's going up forever. So my range numbers are y values that are bigger than or equal to one. I could have y equals 10 and then my x coordinate would way the heck over here. I don't know exactly what my graph does, I don't know all these precise points but I know it goes forever and ever in this vertical direction. So my range could be any number that's bigger than or equal to one.

One more thing to keep in mind, one last idea, is that you want to be really careful that this is a closed circle to show me that it could be, x could be greater than or equal to. If this had been an open circle right there then it would just be strictly greater than. That's one thing to keep in mind based on what you learned about inequalities. So this will get more and more tricky as you go through your Math career but it's really important to remember that the x is the horizontal that represents the domain and the range is the Ys and that's the vertical part of the graph.