Hey, everyone. Make sure that you go ahead and try this example completely on your own before checking back in with me. But here, we're asked to use the graph to estimate the value of each of our limits here. Now the first limit that we're asked to find is the limit of f(x) as x approaches negative 2. Now looking at our graph here, that tells us that we want to look at what our function is doing as x gets really, really close to negative 2 from either side. So looking at our graph here, here is my x value of negative 2. And closing in on negative 2 from that left side, I see that my function seems to be approaching a value of 1. And also coming in from that right side, getting really, really close to negative 2, sort of closing in on it, I again see that my function seems to be approaching 1. So that tells me that my limit of f(x) as x approaches negative 2 is equal to 1. Now let's look at our next limit here. Here, we're asked to find the limit of f(x) as x approaches 0. So again, we want to look at values really, really close to 0 from either side, sort of closing in on it. Now, on our graph here, if we approach 0, getting really, really close to it from that one side, I see that my function seems to be approaching a value of 0. Then coming in from the other side again closing in on that x value of 0, I again see that my function seems to be approaching a value of 0.

So that's what my limit is. Now, here, you might get tripped up by that hole in the middle of our graph because when x is 0, it seems like our function is not defined. There's a hole in our graph. But remember that it does not matter what the actual value of our function is at 0, just what it's doing as x gets really, really close to 0. So don't let that hole freak you out and go ahead and just remember that your limit is as x approaches 0, not when it is 0. Now let's look at one final limit here. We're asked to find the limit of f(x) as x approaches 3. Now looking at 3 on our graph here, wanting to close in on it from either side, our x value of 3 I see here coming from this left side, then my function seems to be approaching a value of 1. Then coming in from that right side, I see the same thing happening. My function is approaching a value of 1. So my limit of f(x) as x approaches 3 is equal to 1.

Now, looking at this graph, you might already start to see that we have a sort of crazy thing happening over here. And if I would have asked you to find the limit as x approaches 4, you might get a little bit tripped up because from this side, I see that we're approaching 1. But from this side, we are not approaching 1. Now, I'm going to show you exactly how to deal with that coming up next in our next video. So I'll see you there. Thanks for watching, and let me know if you have questions.