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Sketch the graph of an example of a function $f$ thatsatisfies all of the given conditions.$\lim _{x \rightarrow 0 \atop x \rightarrow 0} f(x)=1, \quad \lim _{x \rightarrow 3^{-}} f(x)=-2, \quad \lim _{x \rightarrow 3^{+}} f(x)=2$$f(0)=-1, f(3)=1$

Graph of $f(x)$ that meets the given conditions.There are many possible solutions.

Calculus 1 / AB

Chapter 1

FUNCTIONS AND LIMITS

Section 3

The Limit of a Function

Functions

Limits

Continuous Functions

Campbell University

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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so we're gonna be making a graph that has all of these traits. There's many different ways you could go about this one. I'll try to explain the way that I do mine. So first, let's set up our access, and it looks like the points of interest arranging from about negative burrito positive free. So let's disco that are so 123123123 and 123 So let's start with the two fixed points. That's the easiest one. F zero is negative. One. I'll switch colors, so point here, and F A free is equal to positive one. Now the limit as X approaches zero is one. That means as this craft approaches zero, it should be approaching some invisible hole that is right here on draw the invisible hole in a different color. But it's not a part of our grab right here, and it needs to be approaching it from both sides. Now let's look at the next point X approaches free, but from the negative side of the left side, it's going downward to negative two. And then I'll draw a line to the left a little bit and free from the pilot of Side is approaching positive till so do something like that. Now let's go back to my graft color, and we just need to draw a line that touches all of this stuff. What we could Dio is something like this and then something like this. It doesn't say in the problem that it can't be a piece wise functions that is completely acceptable. But this is just one graph. You could have done this since this problem could be done multiple ways.

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