Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

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

06:35

Question

Answered step-by-step

Problem 9 Easy Difficulty

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

$ f(0) = 3 $, $ \displaystyle \lim_{x \to 0^-} f(x) = 4 $, $ \displaystyle \lim_{x \to 0^+} f(x) = 2 $, $ \displaystyle \lim_{x \to -\infty} f(x) = -\infty $, $ \displaystyle \lim_{x \to 4^-} f(x) = -\infty $, $ \displaystyle \lim_{x \to 4^+} f(x) = \infty $, $ \displaystyle \lim_{x \to \infty} f(x) = 3 $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Leon Druch
Numerade Educator

Like

Report

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

More Answers

03:16

Daniel Jaimes

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Related Topics

Limits

Derivatives

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Samuel Hannah

University of Nottingham

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Join Course
Recommended Videos

0:00

Sketch the graph of an exa…

05:49

Sketch the graph of an exa…

0:00

Sketch the graph of an exa…

0:00

Sketch the graph of an exa…

0:00

Sketch the graph of an exa…

0:00

Sketch the graph of an exa…

04:20

Sketch the graph of an exa…

05:04

Sketch the graph of an exa…

01:17

Sketch the graph of an exa…

04:17

Sketch the graph of an exa…

03:57

Sketch the graph of an exa…

0:00

Sketch the graph of an exa…

0:00

Sketch the graph of an exa…

0:00

Sketch the graph of an exa…

04:15

Sketch the graph of an exa…

02:05

Sketch the graph of an exa…

01:44

Sketch the graph of an exa…

0:00

Sketch the graph of an exa…

0:00

Sketch the graph of an exa…

0:00

Sketch the graph of an exa…

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

played a few uh restrictions for starters f of zero equals street. So when x zero D function value is tree, so that's this point right here. Uh The limit of F a bex, as X approaches zero from the negative side is four. So as X approaches zero from negative side to function is going towards four doesn't hit it because at X equals zero to function is here. Um So we're going to be approaching uh the value of for will put an open circle there. Uh As X approaches zero from the positive side, uh F of X is going to approach to so open circle there. Uh the only point on the function when X0 is up here at three. Um as X approaches for from the negative side to function is going to go down towards negative infinity. So we're going to have an ass um Toque line at X equals four. And uh so as X approaches for from the negative side to function goes down towards negative infinity. As X approaches for from the positive side of function is going to go up towards positive Last but not least as x goes towards infinity, Alphabet's approaches three. So let's see if we can draw a function that contains all these situations. As X approaches zero from the negative side to function approaches for sort of function is going to be approaching for As X approaches zero from the negative side and to the left, when extra approaches negative infinity to function uh approaches negative infinity. So we're going to have something that looks like this, Alright, as X approaches zero from the positive side, the function is approaching two. Um But then as X approaches for from the negative side, uh the function goes down towards negative infinity. So it looks like we're going to have something like this and uh we'll check all this one we're done. Uh one item at a time. But now as X approaches four from the positive side to function goes towards infinity. And as X approaches positive infinity, allowing the positive X access to function approaches trade. So approaching four from the positive side, function goes up towards positive infinity. X approaches positive infinity. uh to function approaches three, which is this ascent Opine right here. So I believe this is what our function F of X should look like. Let's read through each restriction and see if it satisfies it. Uh F of zero is three. So when X zero, a point on the graph of F of X right here, at three, as X approaches zero from the negative side to function is approaching for. So as X approaches zero from the left side, the function approaches for open circle because it doesn't hit it. As X approaches zero from the positive side to function approaches to as X approaches negative infinity, the function itself goes down towards negative infinity. As X approaches four from the left from the negative side to function goes down towards negative infinity. As X approaches four from the positive side to functions going up towards positive infinity last, but not least as X approaches positive infinity, to function approaches a value of three.

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.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
191
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
81
Hosted by: Alonso M
See More

Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

Campbell University

Caleb Elmore

Baylor University

Michael Jacobsen

Idaho State University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Join Course
Recommended Videos

0:00

Sketch the graph of an example of a function $ f $ that satisfies all of the gi…

05:49

Sketch the graph of an example of a function $f$ that satisfies all of the give…

0:00

Sketch the graph of an example of a function $f$ that satisfies all of the give…

0:00

Sketch the graph of an example of a function $f$ that satisfies all of the give…

0:00

Sketch the graph of an example of a function $ f $ that satisfies all of the gi…

0:00

Sketch the graph of an example of a function $ f $ that satisfies all of the gi…

04:20

Sketch the graph of an example of a function $ f $ that satisfies all of the gi…

05:04

Sketch the graph of an example of a function $f$ that satisfies all of the give…

01:17

Sketch the graph of an example of a function $f$ that satisfies all of the give…

04:17

Sketch the graph of an example of a function $ f $ that satisfies all of the gi…

03:57

Sketch the graph of an example of a function $f$ that satisfies all of the give…

0:00

Sketch the graph of an example of a function $f$ that satisfies all of the give…

0:00

Sketch the graph of an example of a function $f$ that satisfies all of the give…

0:00

Sketch the graph of an example of a function $ f $ that satisfies all of the gi…

04:15

Sketch the graph of an example of a function $ f $ that satisfies all of the gi…

02:05

Sketch the graph of an example of a function f that satisfies all of the given …

01:44

Sketch the graph of an example of a function $f$ that satisfies all of the give…

0:00

Sketch the graph of an example of a function $\bar{f}$ that satisfies all of th…

0:00

Sketch the graph of an example of a function $ f $ that satisfies all of the gi…

0:00

Sketch the graph of an example of a function $ f $ that satisfies all of the gi…
Additional Mathematics Questions

01:55

"Quadrilateral KMPT Is dilated by & scale factor of 3 to create qua…

01:15

'Find the length of arc CD.
12
80o'

01:02

'In kite PQRS , mZPQR = 780 , and mZTRS = 590 . Find mZQRT'

01:26

'In a class of 25 students, 3 2 of the class are boys, of 5 5 the class…

02:12

'Quesliom
Directions Label the diagram with the following values; th…

01:41

"Juanita is 1.6 meters tall, wants to find the height of a tree in her …

01:04

"REVIEW QE CONCEPTS PL to P'L' by a scale factor of 3. Given …

02:59

'*5) What are the lengths of sides m and n?
m
n'

02:25

'The length of the curved part of a semicircle is 25.12 inches What is …

01:00

'Complete the squares in order to write the equation of the circle Then…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started