Help with continous line graph (interval notation)

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Homework Help Overview

The discussion revolves around determining the interval notation for a continuous line graph, with participants exploring the nature of continuity and discontinuity in the context of the function represented by the graph.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants attempt to express the intervals of continuity but express uncertainty about the correct notation. Questions arise regarding the function's value at specific points, particularly at x = 0, and whether the function is defined there. Some participants discuss the implications of discontinuities and the criteria for continuity.

Discussion Status

The discussion is ongoing, with various interpretations of the problem being explored. Some participants have provided guidance on understanding continuity and interval notation, while others express confusion about the requirements of the exercise. There is no explicit consensus on the correct interval notation, but some clarity has emerged regarding the nature of the function's continuity.

Contextual Notes

Participants note that the problem's phrasing may have led to misunderstandings, particularly regarding the definition of "continuous line" and the expected output in interval notation. There are references to specific discontinuities and the challenges of representing them accurately in notation.

Torshi
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Homework Statement


See attachment: what is the interval notation of the continuous line

Homework Equations


no equation

The Attempt at a Solution



(-2,-1)U(-1,inf) ? not sure then it goes to 1 then to -inf? There are two continuous lines
(-2,-1)U(-1,1)U(1,inf)? No...
i feel like an idiot on this problem
 

Attachments

  • 7c93a0372edb3d4679891d4f3efb1bf8-4567-sethomework_02prob1image1.png
    7c93a0372edb3d4679891d4f3efb1bf8-4567-sethomework_02prob1image1.png
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Last edited:
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Torshi said:

Homework Statement


See attachment: what is the interval notation of the continuous line


Homework Equations


no equation


The Attempt at a Solution



(-2,-1)U(-1,inf) ? not sure then it goes to 1 then to -inf? There are two continuous lines
(-2,-1)U(-1,1)U(1,inf)? No...
i feel like an idiot on this problem
What is the function's value at x = 0 ?
 
SammyS said:
What is the function's value at x = 0 ?

idk inf?
 
Torshi said:
idk inf?
∞ is not a permissible value for a function.

Is the function even defined at x = 0 ?
 
SammyS said:
∞ is not a permissible value for a function.

Is the function even defined at x = 0 ?

Sorry and no it's not I believe. Nothings there. From -1 there is discontinuity and a jump to 1
 
Last edited:
I'm really having trouble with this problem
 
Last edited:
Torshi said:
bump

Read the Forum rules regarding bumping.
 
Torshi said:
Sorry and no it's not I believe. Nothings there. From -1 there is discontinuity and a jump to 1
The function is not defined at x=0, so how can it be continuous there? (You said it was continuous on (-1,1) . )
 
SammyS said:
The function is not defined at x=0, so how can it be continuous there? (You said it was continuous on (-1,1) . )

I'm stuck after (-2,-1) if that's even right for the first continuous line

So there is a hole after -1. Then there is jump to 1 so that (-1,1) doesn't apply since at 0 it's undefined. So from 1 onto where? at 1 there are 2 holes, one going infinitely down and another that goes right

Not continuous:
1.) not defined
2.) limit DNE
3.) limit does not equal to evaluation --> is this the problem? this last one
 
  • #10
(-2,-1)U(-1,0)U(0,1)U(1,3)U(3,4) ? Nope.. How do I do this?
 
Last edited:
  • #11
Torshi said:
I'm stuck after (-2,-1) if that's even right for the first continuous line

So there is a hole after -1. Then there is jump to 1 so that (-1,1) doesn't apply since at 0 it's undefined. So from 1 onto where? at 1 there are 2 holes, one going infinitely down and another that goes right

Not continuous:
1.) not defined
2.) limit DNE
3.) limit does not equal to evaluation --> is this the problem? this last one
What do you mean by "continuous line" ? You're looking for continuity over a set of intervals.


Torshi said:
(-2,-1)U(-1,0)U(0,1)U(1,3)U(3,4) ? Nope.. How do I do this?
Why do you say the graph is not continuous at x=3 ? (Which of the three above reasons?)
 
  • #12
I know the answer finally. The problem was that I had it all along, but everytime I typed it into the box online it would not recognize it due to simple [] in which that's why I was so confused...

The answer is: [-2,-1)U(-1,0)U(0,1)U(1,4]

-Thanks
 
  • #13
SammyS said:
What do you mean by "continuous line" ? You're looking for continuity over a set of intervals.



Why do you say the graph is not continuous at x=3 ? (Which of the three above reasons?)

(1,4]

The previous answers I was posting was simply out of confusion since I've typed in the right answer before and was marked as incorrect, hence my confusion.

Thank you
 
  • #14
Torshi said:

Homework Statement


See attachment: what is the interval notation of the continuous line


Homework Equations


no equation


The Attempt at a Solution



(-2,-1)U(-1,inf) ? not sure then it goes to 1 then to -inf? There are two continuous lines
(-2,-1)U(-1,1)U(1,inf)? No...
i feel like an idiot on this problem

I'm not sure that the people who replied in this thread even understood what the problem is. "Interval notation of the continuous line" makes no sense whatsoever.

Were you supposed to write interval notation for the graph you attached?
 
  • #15
Yes, writing the continuous line in interval notation. Which if done right you can identify the jumps or moments of discontinuity.
 
  • #16
Torshi said:
Yes, writing the continuous line in interval notation.
That's not what I said. The goal of the exercise, I believe, was to write the domain of the function in interval notation.
Torshi said:
Which if done right you can identify the jumps or moments of discontinuity.
 
  • #17
Mark44 said:
That's not what I said. The goal of the exercise, I believe, was to write the domain of the function in interval notation.

Yes, but it didn't state that specifically in the problem. It simply just said write in interval notation of the continuous line and if there is more then one interval use a union sign. It's fine now though, I figured out the answer and the main reason why I couldn't figure it out was because the site wanted a bracket at the beginning and end, simple mistake which confused me into thinking one of the right answers I plugged in didn't work. I believe the other users knew what my question was because they were guiding me in the right direction.
 

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