Hello we're going to talk about functions. Every input has exactly 1 output. On a function there's a correspondence between the first set, the input and the second set, the output. The input is usually referred to as our domain, and on a graph it's usually thought of as the X values or the obscissa, and the output is referred to as a range or the Y values on a graph which are the ordinate abscissa and ordinate, the domain being the input there. For every input, there's exactly 1 output for it to be a function. Function notation F of X, F of X we can think of as similar to our Y, but the F of X is very powerful because it already tells us that this relationship or correspondence exists. F of X tells us already that every input X is going to have exactly 1 output. Frequently people think of F of X as equaling Y. F of X is actually much more powerful than Y because it tells me already that every X has exactly 1 Y. Another notation that is frequently seen is F: X. The X here being the input and the Y being the output, the X here being the domain. And if we had that equaling Y, our Y would be our range. We're next going to look at an example of a graph trying to figure out what this means notation wise. If I ask you what is F of one, what I'm really asking is when X is one, what is Y or F of X? So when we look at this graph and we say F of one, we're going to come and we're going to look when X is one up this vertical line. Here we want to know what's the Y value? Well, the Y value appears to be 7. So when X is 1, the Y is 7. Same kind of graph, different question. What's F of X equal to? So what that's really saying is when Y is 2, what's the X value? And we may have more than one value. So when Y is 2, we're talking about a horizontal line. Here's Y equal 2, and we want to know what X values give this out. So if we look here, it looks like 8 and it looks like -4 So F of eight equal to also F of -4 equal 2. So that's how we interpret F of a number versus F of X equaling a number. The last thing we want to talk about in this segment is a vertical line test and to look at a graph and determine if a graph is a function or not. We need to determine can we stick any vertical line anywhere on the graph and have it only pass through the graph one time. So when I look at this first graph, which is the one we just used in the previous example, any vertical line I put on here only passes the graph one time. So this one is a function. If we look at the graph on the right, when I put in a line, any vertical line, it passes more than one time. The fact that one line passes through the graph more than one time means it's not a function. If we look at the next example, every vertical line I put in appears to only cross the graph one time, so it is a function. I'm looking at our last example. If we look here, it appears to be a function if I'm looking off to the right, but what happens if I come closer to the left? One line is all it takes to make the entire graph not a function. The fact that this one vertical line pass the graph twice makes it not a function. Thank you and have a great day.