Problem

Sketch the graph of an example of a function $f$ …

05:04

Problem 3 Easy Difficulty

Sketch the graph of an example of a function $f$ that satisfies all of the given conditions.
$$\lim _{x \rightarrow 0} f(x)=-\infty, \quad \lim _{x \rightarrow-\infty} f(x)=5, \quad \lim _{x \rightarrow \infty} f(x)=-5$$

Answer

SEE GRAPH

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Calculus 1 / AB

Essential Calculus Early Transcendentals

Chapter 1

FUNCTIONS AND LIMITS

Section 6

Limits Involving Infinity

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Video Transcript

No, Because it's this graph year. Right now, these are the negative attitudes. Negative one negative to negative. Three is are the positive values 123 for this is just a sketch. Now, as you're approaching this season zero the center here is a zero the origin. Right. So as you're approaching zero, you can see that the function here from here going it is approaching infinity here, as you're approaching zero to function is approaching infinity. Right, So limit X approaches. Zero off the function and seclusion. Infinity! So, for example, let's say you here. This is, um, negative 0.1 if you move closer. Negative 0.1 You know, it goes a little bit further to infinity. So you see that as you go, you're approach zero here, the function keys going toe slide in town. But it does not touch the y axis. Right? That is immunity actually acts ass in Tut's right. It is not really touching, but it is lighting tonalist infinity, right? And as you approach negative infinity so the limit as X approaches Negative infinity! So negative Infinity is this point. As you continue to go forward here, continue to fear tourist that left side. What is happening to the function? The function is also, you know is approaching is approaching. Um thank positive Five, right. It's approaching positive. Five. This is a function. Here is a pollution positive fire because here is positive five, right? Positive five is somewhere in between us. So as you continue to go, he are not unknown. Tonto left side and a function is also approaching positive file. And then if it continue to veer too the right side of things, right? As you continue to veer to the right side. So as we continue here along this point 123 4000 going forward as I continue to approach positive infinity than the function here also approaches. Um negative five. Right? Cause 95 is between negative six negative for right. So the function also pushes negative five

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