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in this problem, we was just sketched the graph
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of a function f that satisfies the following. We
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want that every negative too is equal to zero.
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We want the f of positive two is equal to
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zero that the limit as X approaches negative too is
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equal to zero and that the limit is X approaches
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positive to does not exist. So I would like
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to start off with the function values that we know
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we know, regardless of what the function, really
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. They look like that half of negative, too
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zero and so is awful, too. So we
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can kind of at least fill in those coordinates here
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to get us started. So as stated in the
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function, Um, I'm sorry in the question statement
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, there are many correct answers. Was problem infinitely
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many actually. So we just need to provide one
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of those. So the answer you get is a
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little different from this one. That's expected because there's
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a lot of different graphs you could draw that will
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satisfy these conditions. So So now we have one
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and two done, and now I have to take
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care of the limits. So we know that the
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limit is ex purchase Nick if 20 So that tells
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us right away that the limit exists and it's also
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equal two the value of the function there. So
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that's equal to half of negative, too. So
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that tells us our graph is going to look pretty
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smooth here so it can kind of do something like
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this. Essentially, we know there's no breaks in
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the graph there. So two more biscuit work.
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We were not told anything about any other X values
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. Besides, positive to civil kind of fill in
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the graph until you get here and then decide what
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to do. So now we know that the limit
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as X approaches positive to just don't exist. So
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that means this Lim is certainly not equal to f
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of positive, too. So we don't want to
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draw something smooth. But we want something where the
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limit one exist. So as X approaches positive too
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, we can make our craft go towards one of
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the infinities, or it can go in two different
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directions out and so on. So there's a few
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ways we can go about this. Hey, so
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to make the limit not exist here, we can
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make the left limit equal to two. And let's
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say the right Lim. It's approaching three. So
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since the left and right limits do not exist or
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sorry, do not agree, we would say the
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limit as X approaches to does not exist. So
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now we can see that all of our criteria are
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met, and this is one way to answer this
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question.