Problem

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

View

Question

Answered step-by-step

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.

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Mary Wakumoto

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

um Okay so we have kind of a interesting problem. We have two parts to the problem and the first part has to do with can can a function Y equals F. Of X intersect a vertical ascent toad. And so that's an interesting question. Um Usually the answer would be no. Um For example, if I write a function as let's say um one over X -1, then we get the graph that has a vertical ascent toad at one because they're not allowed to have the denominator go to zero. And it turns out that we get a graph, something like this. So notice we have a vertical as um toad and we don't cross the vertical as um toad. So a typical function would not allow you to cross. However, I could define a piecewise function that is for example one over X -1 for any location except at one because this is at X equals one where the ASM toad is and um go ahead and define say f. Of X zero at X equals one. So it wouldn't be exactly intersecting like crossing, but it would be physically on top of the vertical assam toast. So I would say in general no but if we're gonna count um actually being right on top, I can certainly define a point to go right there. But so that's kind of an interesting question. Um And the next part is really part of the same part is then kind of the similar question can Y equals F. Of X intersect um a horizontal a horizontal assam tow and this is definitely true. So um so for the first one I would say usually not. Um and for this one I would say yes it can happen. So for example, if we have, I pulled this one out, Just found a convenient one. If y equals three x squared -1 -2 over five x squared plus four x plus one. Then we get a just a Russia shape of the graph. Um As something that looks like with an innocent toad here At three fists. They have some toads at three fists. But then our graph looks something like this, it actually goes like above and then it goes down below and then it goes like this. So it definitely has the horizontal assume tote but we can cross it. Absolutely. So the second part. Absolutely yes. Alright, I'm going to clear the screen so we can do part B. So I will um Alright, so the second half to the question has to do with the maximum number of horizontal asuntos. And I'll answer clearly. It's too and the reason is is that to find a horizontal absent absent toad. You either check your function going to infinity and you can only get a single value or your check your function going to minus infinity. And uh a great example of a function that has two is Y equals or to make it Y equals ffx but it's inverse tan effect. This is a great function. Um If you ah if you graph it, you will find out that the assassin toads are the horizontal as some toads is. We have one at Positive pi over two and another at negative pi over two. And the function actually looks something like this. It's a pretty cool function goes like that. So um So there's an example of two horizontal sm totes uh in one function. So, anyway, hopefully that helped have an amazing day.

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

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

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

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Catherine Ross

Caleb Elmore

Samuel Hannah

Joseph Lentino

Calculus 1 / AB Courses

Recommended Videos

Watch More Solved Questions in Chapter 2

Video Transcript

James Stewart

Calculus: Early Transcendentals

Catherine Ross

Caleb Elmore

Samuel Hannah

Joseph Lentino

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

Calculus: Early Transcendentals

Catherine Ross

Caleb Elmore

Samuel Hannah

Joseph Lentino

James StewartCalculus: Early Transcendentals

Catherine Ross

Caleb Elmore

Samuel Hannah

Joseph Lentino

James Stewart

Calculus: Early Transcendentals