Problem

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

04:20

Question

Answered step-by-step

Problem 5 Easy Difficulty

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

$ \displaystyle \lim_{x \to 0} f(x) = -\infty $, $ \displaystyle \lim_{x \to -\infty} f(x) = 5 $, $ \displaystyle \lim_{x \to \infty} f(x) = -5 $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Leon Druch

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

Okay, in this problem we want to sketch a function F of x. Uh that satisfies the three given conditions in the problem. Uh First the limit as X approaches zero of our function is negative infinity. So as we approach zero from the right side and from the left side, uh the function is going down towards negative infinity. Okay, so Near 0 to function needs to be going down towards negative infinity from both sides of zero. But before we draw that in uh I want to look at a couple of restrictions. Uh the other condition, the limit of the function as X moves towards negative infinity is five. So his ex moves towards negative infinity. The function goes near five. So his ex is moving to the right, The functions going near five. So let's draw that little portion it as X moves to the left towards negative infinity to function goes towards five. So here you have as X is approaching negative infinity to function is approaching the value of five. Um as X approaches zero, the limit of the function as X approaches zero was negative infinity. So as we approach zero, as X approaches zero to function needs to move down towards negative infinity. So as we get closer to zero, X equals zero to function goes down towards negative infinity. Okay, so let's continue this curve here. So his ex moves closer to zero to function is heading down towards negative infinity. Now, don't forget, as X approaches uh zero Fund a positive side. Uh the function still has to move down towards negative infinity. And that's because if the limit as X approaches zero of our functions negative infinity. Uh That means uh to function has to go down towards negative infinity as we approach zero from both sides from the left side of zero and from the right side of zero. But before we start drawing this, let's look at our third condition. The third condition says the limit of our function as X moves towards positive infinity is negative five. The limit of F of X as X approaches infinity is negative five. So as X approaches positive Phineas, ex moves to the right, The function approaches -5. But don't forget as X approaches zero, the function has to go towards negative infinity. So as we're getting close to zero, the functions going down towards negative infinity. And as X is moving to the right, the functions going towards uh negative five. So we want something that kind of is going to get drawn in like this celeste draw that as we get close to zero to function is going to be dropping down towards negative infinity. And as Ex moves towards the right towards positive and funny, the function is going to get close to negative fuck. Alright. So here this blue graph is the graph of a function F of X that satisfies the conditions as ex moves towards negative infinity to limit of a function will be five. As ex moves towards zero. The limited function is negative infinity, it's dropping down steeper and steeper and steeper. As ex moves towards positive infinity. To function approaches -5.

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