Multiple Choice Question about Modulus Function

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Homework Help Overview

The discussion revolves around a multiple choice question concerning the properties of a modulus function, specifically f(x) = |2x + 4|. Participants are tasked with identifying which statement about the function is false, while also seeking clarification on the concept of continuity and the process of finding derivatives.

Discussion Character

  • Conceptual clarification, Assumption checking, Exploratory

Approaches and Questions Raised

  • Participants explore the meaning of "continuous everywhere" and its implications for the function. There are attempts to understand the derivative of the modulus function and its graphical representation. Questions about the definition of continuity and the process of differentiation are raised.

Discussion Status

The discussion includes various interpretations of continuity and attempts to clarify the derivative of the function. Some participants have provided guidance on how to visualize the function and its derivative, while others express uncertainty about their understanding of the concepts involved. There is a suggestion that one of the statements (specifically B) may be false, but this is not universally agreed upon.

Contextual Notes

Participants indicate that they may need to revisit foundational concepts related to continuity and differentiation, suggesting that these topics were covered previously but may require further review.

Atheismo
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Homework Statement



Multiple choice question about a modulus function, which statement is false?
Below is the multiple choice question about a modulus function (the domain of the function is all reals):

Which one of the following is not true about the function f(x)= | 2x+4 | :

A. The graph of f is continuous everywhere
B. The graph of f ' is continuous everywhere ( f ' is the derivative of f)
C. f(x) is greater than or equal to zero for all values of x
D. f '(x) = 2 when x > 0
E. f '(x) = -2 when x < -2

End Question

Can someone please tell me the correct answer and why. Also, please explain to me what "continuous everywhere" means.

Thank you.
 
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Continuous everywhere means that f is continuous at each point.

Draw a graph of this function and draw a graph of its derivative. After you do that, you should be able to figure out which is the false statement.
 
Mark44 said:
Continuous everywhere means that f is continuous at each point.

Draw a graph of this function and draw a graph of its derivative. After you do that, you should be able to figure out which is the false statement.

But what does it mean by f is "continuous"? I don't know what that means.

Also, how do I find the derivative?
 
A continuous graph means you can draw it without lifting your pencil from the paper (one way to look at it).

To find the derivative, rewrite it as |2x+4| = √(2x+4)2, since |x| = √(x2), and use the chain rule.
 
Atheismo said:
But what does it mean by f is "continuous"? I don't know what that means.

Also, how do I find the derivative?
Your book should have a definition of this term, and probably has some examples of functions that are continuous and some that aren't.

If the problem is asking you about the derivative, it's reasonable for us to assume that differentiation has already been covered in your course.
 
Mark44 said:
Your book should have a definition of this term, and probably has some examples of functions that are continuous and some that aren't.

If the problem is asking you about the derivative, it's reasonable for us to assume that differentiation has already been covered in your course.

Yes it has but a while ago. I need to do some revision. I got the answer, I think, it's B right?

Answers D and E give it away lol.
 
Last edited:
Yes, b is the one that is not true.
 

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