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Sketch the graph of an example of a function $f$ that satisfies all of the given conditions.$$f(0)=3, \quad \lim _{x \rightarrow 0^{-}} f(x)=4, \quad \lim _{x \rightarrow 0^{+}} f(x)=2$$ $$\lim _{x \rightarrow-\infty} f(x)=-\infty, \quad \lim _{x \rightarrow 4^{-}} f(x)=-\infty, \quad \lim _{x \rightarrow 4^{+}} f(x)=\infty$$ $$\lim _{x \rightarrow \infty} f(x)=3$$

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Calculus 1 / AB

Chapter 1

FUNCTIONS AND LIMITS

Section 6

Limits Involving Infinity

Functions

Limits

Continuous Functions

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

04:20

Sketch the graph of an exa…

05:04

0:00

03:57

05:32

02:18

02:56

02:45

So how did this nice little sketch here? Eso straight away. What is what is the limit? As executions Negative for from the left right limit X approaches negative for right from the left. So from the left side. So inclusion approaching positive for from the left, right as X approaches positive for from the left. Right. So approaching positive four from the left is like this, right? You're going like that because person before is here. Right? Separation from the letters like that. So if approaching 40 left, what are you gonna hit your hidden? This curve hit in this kind of here? Right? Which is sliding towards negative infinity. You see that? So is sliding toners negative infamy. The function is a current where you have to look at occurs and then what? ISS when you're approaching four from the right right of a function. Still if approaching four from the right off the function right for this year. But when you're pushing for from the right, you hit in this curve, right? And when you hit in discover of where is it? Sliding tours. Well, is it is rising up to infinity, right? As you continue to hit. Continue to get here. You hit this curve and it's raining. Raising up to infinity. Right, So so rises to infinity right now. What is the limit? As you approach zero from the left, this is your right. So if I'm trying to approach zero from the left, what am I hidden? Hidden? Discard? Can you see that? And so where is this curve approaching? Well, it is approaching four. Right, seclusion for cause here is high. So it is approaching for right, cause for is gonna be here than three into, right? So as you continue to hit us function and this function is approaching for here, right, so and take out the air's So this is for right now if you're approaching zero from the right. Well, if a pollution zero from right, what is happening? So this is how you approach zero from the right? Right? So if you approach zero from right, then you hit this particular See the Citrus It dark here. I know that that is to write. Honesty is just not drawn to scale the discussion, but I just you right? So us You hit this zero here from the right hit us to start here, which is to write. So it is just by observation is very simple for you to look at it and then do it right so good. So once you have that, then look at the limit as you approach negative infinity. So the limit as you approach Negative infinity, This is negative. You go snow towards decide. Right? So as you are approaching negative infinity, what is happening to the function? The function is also going because you're gonna as you go here on a result outside, the function is gonna hit this curve, right? And this car is sliding towards infinity. Can you see that it is a straight line slide? And tourists negative infinity, right? Because this is the negative side of why, right? So as you continue to go to infinity for this horizontal side, you hit this curve and in this curve is sliding towards infinity, Right? Deciding towards negative infinity to precise. So this is gonna be negative. Infinity! And what if your approach in, uh positive infinity So the limit as X approaches Positive infinity! So we're approaching positive Infinity, what is happening to the function? But this is how you approach positive infinity, right for the horizontal side. What happens to the function? Well, you hit this curve as you proceed to positive infinity. You hit this curve, right? And when you heard that this current what is this curve? It is flapping out at three. Right. Here's three here because 234 Right. So it is flattening out at three. Okay, so when you check, the curve is flattening out at three. Right? So this is just one example off the curve, right? You can have a so many examples. It's possible, right? Particularly areas that I was using to do illustration. And you curve alone. So this is a curve, right?

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