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Problem 15 Medium Difficulty

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

$ \displaystyle \lim_{x \to 0^-}f(x) = -1 $, $ \displaystyle \lim_{x \to 0^+}f(x) = 2 $, $ f(0) = 1 $

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Video Transcript

All right. So you want to sketch a function F of X with all three of these conditions. The limit as X goes to zero from the left is negative one limit as X goes to zero from the right is positive two, and the value at zero is positive one. All right. So the function has got to be continuous for a little bit to the left and right of zero. It's probably easier just to make it continuous everywhere except zero. And then these critical values are one, two and negative one. Okay, so what's happening? Let's do the easiest part at zero. The value is one. So it's got to pass through that point to the left of zero. It's gotta approach negative one. So it's not going to be a negative one and zero because it's already 1 to 0, it's just got to do something and end up at negative one. And then to the right, we've got to approach positive to it's not going to be too so that's an open circle. The function is just going to do something and approach to so there is one