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Sketch the graph of an example of a function $ f $ that satisfies all of the given conditions.

$ \displaystyle \lim_{x \to 2} f(x) = \infty $, $ \displaystyle \lim_{x \to 2^+} f(x) = \infty $, $ \displaystyle \lim_{x \to 2^-} f(x) = -\infty $, $ \displaystyle \lim_{x \to -\infty} f(x) = 0 $, $ \displaystyle \lim_{x \to \infty} f(x) = 0 $, $ f(0) = 0 $

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Arthur S.

June 1, 2019

Hi great work!

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We want to sketch the graph of some function f that satisfies a few different conditions. Now, the one will start with, since it's probably the easiest is f of zero equals zero. So all we have to do is place a zero. The next one I'll do is the limit as X approaches negative infinity of F f x equals zero. So what this means is as X approaches negative infinity. So as we get smaller and smaller In the graph of F of X should get closer and closer to zero. Now on the positive side, as X approaches positive infinity, uh we still want the limit to be zero. So as X gets larger, you're going to have the graph of X get closer and closer to zero. Now, as we approach to from the negative side, as the limit of X approaches to from the negative side of F of X equals negative infinity. So as we get closer to two, the graph ffx gets smaller and smaller, and we go down towards negative infinity. And then as we approach to from the positive side, um the graph gets larger as we're going towards positive infinity. So this is a sketch of a graph that should meet all of these limit conditions.