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For the function whose graph is given, state the following_Iimlim fx)limthe equations of the asymptotes (Enter your answers as comma separated list of equations:)ve...

Question

For the function whose graph is given, state the following_Iimlim fx)limthe equations of the asymptotes (Enter your answers as comma separated list of equations:)verticalhorizontal

For the function whose graph is given, state the following_ Iim lim fx) lim the equations of the asymptotes (Enter your answers as comma separated list of equations:) vertical horizontal



Answers

$$ \begin{array}{l}{\text { For the function } f \text { whose graph is given, state the following. }} \\ {\text { (a) } \lim _{x \rightarrow 2} f(x)}\end{array} $$
$$ \lim _{x \rightarrow-1^{+}} f(x) \quad \text { (d) } \lim _{x \rightarrow \infty} f(x) $$
$$ (e) \lim _{x \rightarrow-\infty} f(x) $$ (f) The equations of the asymptotes

So this problem asks us to find the limits at various values of some function. F of X, which has multiple vertical, asked oats. So part A. How's this? Looking at X is equal to negative seven. So let's draw little diet down here. But it looks like you have this practice line represent that this line represent X equal to negative seven, then affects from the West. What? Something like this and from the rate of something like this so part today we want to find a limit. Uh, the effects at X is equal to negative seven and we can see that sense from the left half of bags approaches negative infinity and from the right it approaches negative infinity as well, Then this limit is simply negative. Infinity Part B has us looking at X is equal to negative three. So similarly, let's let this line represents thanks to you called a negative three and you can draw off the text of something like this. Uh, and this problem also wants us finding the limit as X approaches. Negative three of FX. Uh, and so we just tried for the last three seasons. And Quebec's a purchase positive affinity from the right awesome practice, Pilot of infinity. And thus this limit is just infinity. Part C has us looking at, uh X is equal to zero. So again but this line represent access equal to zero. And at the back looks something like this around in X is equal to zero. So we want to find a limit as X approaches zero of f of X and so we can just track again from the left purchase infinity from the rank. It also approaches infinity. Therefore, the limit is just infinity now part indeed, We're looking at first D and e we're looking at X is equal to six So we let this long, meaningful negative six for equal positive six. By about uh then we look at ffx It looks something like this Now Part D we want to find the limit from the left. So the limit as X approaches six from the left of the backs and we just facts on the left. We see these approaches Negative infinity similarly party. We want to find the limit as X approaches sex from the road So we track after that from the room Mhm missing approaches. Positive Infinity Now part of us. We want to find all equations of vertical ascent. It's and so here we can just go back. Look at all the other parts we've done. These are all the values of the vertical acid toots shown in the graph of FX. So we have X is equal to negative seven from part A X is equal to negative three from part B X is equal to zero from part C and X is equal to six from parts DND. So those are the equations. X is equal to negative. Seven X is equal to negative. Three X is equal to zero. X is equal to sex and these the values of the equations of the vertical asset it's

So this problem asks us to find, uh, the limit of a function of X, had various values, uh, and this function a vexes and asymptotic function. So for part A, we're looking at the Value X is equal to negative. And so we have this line representing is equal to negative three. Can we see that from the left? A of Mexico's like that and the right he goes something like that. And so as dilemma has X approaches negative three of a of X. But from the left, we see that approaches infinity from the right. It also approaches infinity on these asthma tubes. So therefore, we can say that for part A, the limit is equal to infinity. Similarly, for part B, we're looking at the value of X is equal to two. So let this line represents X equal to two on the left and expect something like this from the right. Something like this. So, per b, we want to find, uh, the limit as X to purchase two from the left. But we can look at this part of FX the left of exit they go to you see, it approaches negative infinity as it gets infinitely close to X is equal to. Therefore, that's the limit of B, but perceive we want to find to limit as X approaches to from the ring. So we just go a long trek the right side the next equal to 2.5 X and we see conversely, it approaches positive infinity. So that's the limit for seed. Now, for part D, we want to find the limit as X approaches. Negative one. And they're the graph looks something like this where this line represent X equal to negative form. AMX was like that from the left and that from the right and we just want to find we don't want to. We just want to find the limit as X approaches negative one BMX and since similarly, similarly as part A. Since the left side approaches negative infinity and the right side approaches negative affinity, they're both approach negative infinity and therefore that is the limit. I mean X now Part E asked us to find all values of vertical ascent toads the effects shown on the graph and we can just go back on our previous parts here and find all the values where they were ass and tits that we saw. So we have X is equal to negative three from part A X is equal to two from part parts B and C and X is equal to negative one from party. And all of these values are a sentence. So therefore these would be the values and there are none others shown on the grass, and that is the answer for party.

Okay. This question wants us to find all Assam totes for this function. And I just made a rough sketch copping it from the book here. And first, we're going to find all the vertical Assam totes and looking at this graph, there aren't any points of dis continuity where it jumps to positive or negative infinity. So there are none. Then for the horizontal Assam totes, we have to look at the end behavior for this function. So for the minus infinity direction, we see that the limit is just going to be zero because this red tail of the function just approaches the X axis. So why equals zero is our Assam toe in that direction and then for the positive infinity direction, Well, it's not approaching a certain value. It's actually blowing up towards infinity. So there isn't an Assam toe in the positive infinity direction horizontally. So that means we just have one horizontal assam toe as we go in the negative direction and no vertical ASAP totes

Okay, This question wants us to find the Assam totes for this graph. So I just made a rough sketch of what's going on here, and we'll start by identifying the vertical Assam totes. So that's any point where the function shoots off towards infinity and we see that dis continuity part is only at X equals 10 because it blows up the positive infinity on one side and negative infinity on the other without crossing. So that's a vertical ASAP tote. Then, for the horizontal Assam totes, we need to find the infinite limits for each side. So we have to look at what the function does as we go to positive and negative infinity in the extraction. So in the negative extraction, we see that it flattens out towards the blue Line, which, based on the book, it says that that line is that why equals one. So that's our horizontal Assen toe in that direction, and then it actually approaches the same line as we go towards positive infinity. So it's y equals one again. So the end behavior in both directions just has our function approaching. Why equals one horizontally and there's just that one vertical Assen toe at X equals 10


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