Problem

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

09:00

Question

Answered step-by-step

Problem 7 Easy Difficulty

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

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

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Anjali Kurse

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Watch More Solved Questions in Chapter 2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Video Transcript

So what we're gonna do here is sketch a graph of a function F that satisfies all of these conditions. So, the the limit ah the limit as X approaches to should be equal to negative infinity. Okay, then, the limit as X approaches infinity should be equal to infinity. The limit as X approaches Negative Infinity should be equal to zero. And the limit to more. The limit as X limit as X approaches zero from the right should be equal to infinity. and limit as X approaches zero from the left limit, as X approaches zero from the left should be equal to negative infinity, negative infinity. Okay, cool, so let's draw a graph with all of those features. Let's start at the ends of the graph. So as X goes off to positive infinity, which is over this way, it's going to keep going. X gets bigger and bigger and bigger. This graph is going to go up to infinity. That looks like more of a line than a curve. Go up to infinity. Cool. Okay then, as X goes to negative infinity, it's going to head to zero. Control it a little better. Zero. Okay. Or I guess either one of these could work. We're gonna have to choose one. Okay, Now, as X approaches to to there's going to be a vertical ascent owed and I know that because from both sides this graph at as X approaches to is going to be heading towards negative infinity just like that. Okay, now, how about has X ghost? So we've taken care of this one. This one this one. Okay. Now, as X approaches zero from the right, that's what that little plus means. This is going to head up do positive infinity. Okay, Now, as X approaches zero from the left, X approaches zero from the left, we're going to get negative infinity negative infinitely. Okay, now we've drawn all the portions we need so let's just play connect the dots so this is going to come up that's really awfully drawn. Okay like that. I'm going to head up deposit you know what, I'm just gonna redraw this part, that's bothering me. Going to head up to Passo infinitely. I know it looks a little funny, sorry about that. Okay and now this one is going to head over to zero and look at that. We have fulfilled all the pieces of the graph. Let's do a quick review. So as X approaches to from both the right and the left, this graph is headed down to negative negative infinity. That works. This is the line x equals two. Okay, now, as X approaches infinity, which is over this way the graph goes up to infinity, yep I could yeah that works okay. Now as X approaches negative infinity this graph is going to go to zero, Which it does heads over 20. The swimming Okay? And then As X approaches zero from the right, we got up to positive infinity here and zero from the left down to negative infinity here. So this red graph with some blacks and blues thrown on there for fun Z's is what this graph is going to look like with all of these conditions satisfied.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem