Multiple Choice Question about Modulus Function

In summary, the conversation is about a multiple choice question regarding a modulus function and its properties. The question asks which statement is false and the options include statements about the graph, derivative, and function values. The concept of continuity is discussed and it is explained that to find the derivative, the chain rule is used. After some discussion, the correct answer (B) is determined.
  • #1
Atheismo
8
0

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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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.
 
  • #6
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:
  • #7
Yes, b is the one that is not true.
 

FAQ: Multiple Choice Question about Modulus Function

What is a modulus function?

A modulus function is a mathematical function that calculates the remainder when one integer is divided by another. It is denoted by the symbol "|" and is commonly used in computer programming and mathematics.

How is a modulus function represented in mathematical notation?

A modulus function is represented as "f(x) = |x|", where x is the input value and |x| represents the absolute value of x.

What is the purpose of a modulus function?

The purpose of a modulus function is to determine the remainder when dividing two integers. It is useful in a variety of applications, such as finding the smallest possible change in a given currency or determining the periodicity of a repeating pattern.

What is the difference between a modulus function and a remainder function?

A modulus function calculates the remainder when dividing two integers, while a remainder function calculates the remainder when dividing two real numbers. The modulus function only works with integers, while the remainder function can work with both integers and real numbers.

How is a modulus function used in multiple choice questions?

A modulus function can be used in multiple choice questions to test a student's understanding of mathematical concepts, such as finding remainders or solving equations involving absolute value. It can also be used to create answer choices that are close in value to test a student's attention to detail.

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