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

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Calculus 1 / AB

Chapter 1

FUNCTIONS AND LIMITS

Section 6

Limits Involving Infinity

Functions

Limits

Continuous Functions

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so have is, uh, sketch here. I can see that as x approaches to you having a vertical ass into. Right. So as you're fruition to hear, you have any vertical vertical asking to eso take this one off. Yeah. So what's your solution? Does to here You can see that A function a solution? Infinity Racer. The Lewit As X approaches to you can have a you know, it's like is gonna continue on and on and on. It's not drawn to scale is just a rough sketch, right? Eso if you're trying to approach negative too from the left, right. If your fortune, if we're approaching two from the left having apartment, not negativity. Yeah. No two. Exactly. If you're approaching negative to from the left, Negative from the left. So fresh in negative from the left is like that, Right, cause this is from the left, right? You're approaching negative two from values that are less than native to. Then as you're approaching 92 you could hide it from us. Working is sliding too negative. And Finney, you see that from going to slide into negative infinity here. So as you're approaching negative to the function is slide into negative infinity. Right? And what about as you're approaching negritude from the right? Pretty negative from the right. Is this direction depression? Negative Two from values that are, uh, bigger than negative to say. So if you're approaching negative too, then you have that, uh, vertical ascent is right. So as approaching native to from the right, what is happening less you as you approach native like this from the right like that. You know, you just your stopping point, right? That's approaching there from the right. Then you can see that you have this thing here, go into infinity, right? Go symphony. Yeah. Good. So Ah, what is a functional value at zero. Right. So here, f at zero functional value and X equals zero, So zero. Right. So you have 00 as a coordinate. Right? This place is 00 here as a warning. Right. So All right. This one Probably. Yeah. Now, um, what is the limit? Asked you approaching Finney, right? As you approach infinity, what is happening to the functional values? So the limit as you approach negative infinity, you can see that it functions is approaching. This is negative. Infinity I'm approaching negative infinity and going Taurus. Just that site. Right? So negative five negative. 10 negative 1000 natives due to one million. So you go like that, right? You're going like that, Affinity. What is happening to the function? Look at a function. The function is sliding. Told receiver, Right? It is almost touching this This horizontal axis here. Right, So the limit as X approaches. Negative. Infinity off the function zero. Right. Because as you move to the left side of functions, almost Russian zero. Right, That's where you can see. And then what is for? No! Get a positive Infinity. The limits as you sly tours Positive infinity on the horizontal axis. Right. Well, who's lad towards Infinity does this? This is the direction you gotta go. I look at this function here is also sliding. Almost tourist zero. It is almost hidden This horizontal axis where? Why is your right? So it is all also zero here, Right, So? So once you have that, you can see that this is just one example off a grand as satisfies all these conditions here, right?

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