Hi, I’m Kendall Roberg, and today we are going to talk about end behavior. Now ever since you were a young mathematician graphing things, you drew little arrows at the end of functions to describe that they continue going on beyond the little picture you just provided. Today, we’re going to talk about a precise way of describing what’s actually happening. Now, end behavior is about describing what happens at the ends of a function. So at the end, right here at this arrow, and at the end over here, at this arrow. And we have to describe what’s happening at each of these ends separately. So we use a little bit awkward of a language, but once you master it, it really isn’t that bad. So let me tell you how we describe this end behavior. We say that the function, or f(x), approaches positive infinity. And we know that because it’s going up; it’s going up, up, up so high that it keeps getting bigger and bigger. So in math, we say f(x) approaches positive infinity. Now, when is it approaching positive infinity? Well, it’s approaching positive infinity as x is increasing. So we say the function approaches positive infinity as x approaches positive infinity. So what we’ve done now is describe what happens to the function as we continue going higher and higher on the x-axis. Now, we need to describe one other side of the function; this side right here. Now, on this side, x is not increasing, x is actually decreasing. So we know what we’re going to write for the second part of the function, but what’s happening to the actual function? Well, in this case, it’s going down, and the way we describe that in f is we say f(x), or the function, approaches negative infinity as x approaches negative infinity. So the x-axis is going towards negative infinity over here, while the function is going down to negative infinity. Let’s try one more. This one has a little bit different of a graph; it kinda looks like a big W. But again, we need to describe the end behavior at the end of each function. So, let’s look at this first one. Well, this first one is when x is approaching infinity, and this one over here is when x is approaching negative infinity, so what’s happening to the function on this side? Well, as x is approaching infinity, the function is also approaching positive infinity, so we say f(x), or the function approaches positive infinity as x approaches positive infinity. So let me point to the words as I’m saying them to help with the translation. In math, we say, “f of x”, the arrow indicates “approaches,” positive infinity as x approaches positive infinity. So one more time: f(x) approaches positive infinity as x approaches positive infinity. Now what’s funny about this graph is actually on the other side the function is approaching positive infinity as well. So we say again that f(x) approaches positive infinity as x, the x-axis, is approaching negative infinity. And we’re done! That’s how we describe end behavior.