>> This function involves a rather peculiar notation and the graph of the function is rather peculiar as well. This notation is the--the notation for greatest integer. So this would be read the greatest integer in X. Now the interpretation of it can be explained by looking at the table of values. Suppose I want to plot some points. Now, the greatest integer in 1 when X is replaced with 1, the greatest integer in 1 is 1. The greatest integer in 1.3, still 1. The greatest integer in 1.7, still 1. The greatest integer in 1.9, still 1. The greatest integer in 2 though, is 2. The greatest integer in 2.5 is 2. Okay, we get the idea here. Now graphically, look at what happens. I've constructed the graph of these points. I plotted these points. Now for X values that are between 1 and 2, the greatest integers for all those numbers, is 1. So we have this graph. But once we get to 2 we are no longer here. We jump up to this--to this point, you see. And for values of X that are between 2 and 3, the greatest integer in those numbers is 2, until we get to 3 and then we jump to 3. And then we go across like and this pattern kinda continues like this. So let's see, this is called a "step function" for perhaps obvious reasons here because of this stair step affair with the graph, kinda neat kind of function. And you might be just thinking, "Gee, where is this ever useful?" Well it turns out that telephone bills are a lot of times described by using step functions. If your telephone charge is on the basis of a particular amount of money for let's say, the first minute and then a particular amount of money, a different amount for every minute thereafter. Well, what happens with parts of minutes? Well it turns out that your charge or the greatest integer in the number of minutes that you talked. Here's what I mean, suppose we're charged 50 cents for the first minute and 36 minutes for each additional minute. Now where do parts of minutes come in? If you talk for 1 minute and 10 seconds, you're gonna be charged 50 cents for that first minute and that 10 seconds in that second minute kicks you over to an additional 36 cents, you see. And so let's write an equation for this and it will be a step function. It's a cost idea or the cost of this telephone charges is 50 cents is the fix charge plus the greatest integer in an amount of time in minutes times 36 cents, you see. Now so for 0 to 1 minute, the greatest integer from 0 to 1 is 0. So for 30 seconds of time you're charged nothing over here. You've got that during that first minute, that's 50 cents idea. And for the next minute, once you jump over 1 minute you're at--excuse me, once you get to the 1 minute mark, then you're changed here. But like for one and a half minutes, you got 50 cents plus let's see, one and a half minutes right here, the greatest integer in one and a half minutes is 1. So it's 1 times 36. You see, even though you're talking for only 1 minute and 30 seconds, you're charged for that as a whole minute, you see, that additional minute. Anyway, that's the function associated with a telephone bill such as this, kind of an interesting and weird situation.