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For the function $ A $ whose graph is shown, state the following.

(a) $ \displaystyle \lim_{x\to -3}A(x) $

(b) $ \displaystyle \lim_{x\to 2^-}A(x) $

(c) $ \displaystyle \lim_{x\to 2^+}A(x) $

(d) $ \displaystyle \lim_{x\to -1}A(x) $

(e) The equations of the vertical asymptotes

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J H.

July 2, 2021

eh

So in this problem we're given this function A has this graph right here and were asked to state the following. So first of all, we're asked to state the limit As X goes to -3 of a f X. And we can see in this graph That -3 over here is actually innocent. Okay. And both the limit As X goes to -3 from the left side of a fx, this goes to infinity and the limit as X goes to minus three from the right side of a of X is also going to infinity. And so therefore the limit his ex goes to money three of a of x is infinity. So the first one is infinity. Now, the next one, the limit as X goes to minus goes to two from the left side they have X. Well, let's look at our graph here for a minute. Here's to and two is also an assam toad here as I go in towards two from the left side, this goes all the way down and keeps continuing on down to minus infinity. Okay, hard to see the limit As X goes to two from the the right hand side of a of X. Well, let's look at our graph again, twos and assam tote and as I come in Towards two from the right hand side, our graph, this asset oats continuing on up towards positive infinity. So this is infinity and then party the limit As X goes to -1 of a of X. Well, let's see As we go to -1 here, Here's -1 right here. And what do we notice this is a vertical asthma tote as well. And whether we come in from The limit as X goes to -1 from the left of a f x is minus infinity, I can draw that better. And that's also the limit As X goes to -1 from the right side of a fx. Because if we look at our graph, both sides Here at -1, go continuing on down to minus infinity. And so the answer for this one is minus infinity. And then part E says equations of the vertical assam. Totes equations of vertical hossam totes. Well, that's everywhere. We have one of those asientos, so that's X equals minus three, X equals minus one, X equals two. Is our three vertical aspect towards that we see occurring here.

Oklahoma State University