Problem

For the function $ f $ whose graph is given, stat…

View

Problem 2 Medium Difficulty

(a) Can the graph of $y=f(x)$ intersect a vertical asymptote? Can it intersect a horizontal asymptote? Illustrate by sketching graphs.
(b) How many horizontal asymptotes can the graph of $y=f(x)$ have? Sketch graphs to illustrate the possibilities.

Answer

More Answers

04:19

Daniel J.

01:22

Carson M.

Topics

Limits

Derivatives

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Catherine R.

Missouri State University

Heather Z.

Oregon State University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

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 in this question we were asked to crast if the function Y equals F of X intersects a vertical ascent. Okay. Yeah. And the answer is no. Hi. And why is that? Well, because Y equals F of X means for all X. In the real numbers there is a why value such that Y equals F of X. Okay, if we have a vertical assam tote then mhm. Then first of all, let's see. Well then why goes to infinity or minus infinity? At Uh huh. At that X. Okay. So there is no. So there is no value of why they're that occurs in other words, why does not intersect all along? Uh huh. X equals that value will call it a. Okay. Then. Were asked if can intersect the horizontal assam toe and the answer is intersect horizontal. Some toast. Yeah. And the answer here is yes. So let's think about a function here for a minute. We'll have our X. And or Y here. And let's say that our function does something like this like this, right? Where we have crossed this horizontal assam. Tote of Y equals zero, Husband crossed here and here and here. So it crossed at least three times with this function Because really the question is when X goes to infinity then Y equals F of X, right? Goes to why call zero is what happens? So you could you can't cross the horizontal assam toe at least once. Well, the function that is possible and still have a horizontal assam tote. It was demonstrated in that graph right there. So how many horizontal assume totes can a graph of Y equals F of X have? How many horizontal have some totes? Uh Some, hang on. MS builders correctly, awesome. Totes can we have? Well, think about it. We can have one as X goes to infinity, then Y equals F of X. Can go to horizontal. Have some tote. So there's one. What about when X goes to minus infinity? We could do the same thing Y equals F of X. Could go to another horizontal assam Tope. So there's a 2nd 1. So thus two horizontal have some totes are possible. Mm. Okay.

DM

David M.

Oklahoma State University

Topics

Limits

Derivatives

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Top Calculus 1 / AB Educators

Catherine R.

Missouri State University

Heather Z.

Oregon State University

Caleb E.

Baylor University

Samuel H.

University of Nottingham