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University of North Texas

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Problem 24 Easy Difficulty

Graph the function using as many viewing rectangles as you need to depict the true nature of the function.

$ f(x) = e^x + \ln |x - 4| $

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Video Transcript

you want to grab the function after taxes, equity, eat of X plus natural olive, the value of X minus four, using as maybe Rick tingles as we need to depict the true nature of the function. So here you can see that I went ahead and already grabbed the Kapu viewing rectangles and of this kind of go through my rationale behind why I chose each of the ones I did. So the 1st 1 here on the left is just from negative. X is equal to negative 30 20. And it gives the overall shape of the graph that we have. And I just kind of found this by zooming out as far as I can, and then the first thing I did once I saw this waas, I noticed that around X is equal to four. So in this region right here, it starts to look like it dips down pretty far. So I went ahead and blew up the area around excessively before to give this first graph right here. And you can see that about right here. It looks like we have a local max four this function, and then it just kind of get dips down at Exeter before, then dips back up. And if you were to just keep zooming in and him about excessive or is just going to look more like this or at least with the graphing calculator that I was using is going to just kind of dip down further further. But we know that if we weren't a Plug X is a good four into here, we get a vertical awesome, too, for the natural law. So X is it before is actually a vertical acid trip. So this should just keep on going down and down forever. And it's some points right here and the latter. How much? I actually zoomed in and I could never actually get it to go there because the closer and closer I get to four, it would just say it would become undefined. So maybe if you had a little bit better graphing calculator, you would also find where, where the ex intercepts where there should be. But it should look something kind of more like this here, as opposed to what we actually okay. And that kind of gives us the behavior amount exit before and unfortunately doesn't give us much information. And the other part that I thought was kind of interesting was over here around X is equal toe negative too. So I went ahead and made this area a little bit larger, and we can see that this point here ends up being a local men. And again, this was at X is about negative. 1.7 are negative. So we can kind of see the local backs and local men behavior here, and something else we might be able to notice is it looks like around here we have a point of inflection. So that's why one had included that. And also in our first round here, you might notice that around our local max, we also have a point of inflection that kind of looks like and to the right here. We also have a point of in election. So these were the three viewing rectangles that I thought were useful for describing no ground of dysfunction