Download the App!

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

Question

Answered step-by-step

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

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Leon Druch

Numerade Educator

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

03:16

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Missouri State University

Oregon State University

Baylor University

University of Nottingham

Lectures

04:40

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.

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.

0:00

Sketch the graph of an exa…

05:49

04:20

05:04

01:17

04:17

03:57

04:15

02:05

01:44

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.

View More Answers From This Book

Find Another Textbook

Campbell University

Idaho State University

01:55

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

01:15

'Find the length of arc CD.1280o'

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

'QuesliomDirections 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?mn'

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…