Drawing the Graph: Analyzing Solutions and Questions

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SUMMARY

The discussion centers on the proper representation of discontinuous electric fields in graphing. Specifically, it emphasizes that vertical lines should not be drawn at discontinuities, such as at x = 1 cm and x = 3 cm, because this would incorrectly suggest that the electric field possesses all intermediate values. The correct approach is to plot the electric field as discontinuous functions to accurately reflect its behavior at these points. This clarification was provided by user @kuruman, reinforcing the importance of accurate graphing techniques in physics.

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Homework Statement
Please see below
Relevant Equations
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For this problem,
1673315233100.png
,
The solutions is,
1673315261826.png

However, why did they not draw vertical lines for the graph like this:
1673315340737.png
?

Thank you!
 
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Callumnc1 said:
However, why did they not draw vertical lines for the graph like this:
Because the electric field is discontinuous at x = 1 cm and x = 3 cm and that is how discontinuous functions are plotted. Drawing a line as you suggest implies that the electric field has all the in-between values which it doesn't.
 
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kuruman said:
Because the electric field is discontinuous at x = 1 cm and x = 3 cm and that is how discontinuous functions are plotted. Drawing a line as you suggest implies that the electric field has all the in-between values which it doesn't.
Got it, thank you @kuruman !
 

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