Why does this happen with my graph?

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Discussion Overview

The discussion revolves around the behavior of the graph of the function f(x) = x/x, particularly at the point x=0, and the implications of graphing software like Mathcad in representing undefined values. Participants explore the nature of the graph, the presence of vertical lines, and the handling of indeterminate forms like 0/0.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that the graph of f(x) = x/x appears to have a T shape with a vertical line starting at x=0, despite being undefined there.
  • Another participant suggests that the graph should have a tiny hole at x=0, indicating that the graphing software may be incorrectly treating the indeterminate form 0/0 as equal to 0.
  • A different participant describes a function A that has a vertical line from y=0 to y=8 at x=0, arguing that this representation makes sense in their context.
  • One participant emphasizes the importance of understanding the output of graphing software, cautioning against blindly trusting its representations without comprehension.
  • Another participant asserts that the function A is undefined at x=0 and argues against the presence of a vertical line, comparing it to a parabolic function that has a hole at that point.
  • Participants discuss the default behavior of Mathcad in defining 0/0 as 0 and mention options to adjust this setting to avoid misinterpretations.
  • One participant raises concerns about potential round-off errors when dealing with functions that approach zero, complicating the analysis of limits and indeterminate forms.

Areas of Agreement / Disagreement

Participants express differing views on the representation of the function at x=0, with some arguing for the presence of a vertical line and others insisting it should be undefined. The discussion remains unresolved, with multiple competing interpretations of the graph's behavior.

Contextual Notes

There are limitations regarding the assumptions made about the behavior of the function at x=0 and the implications of using graphing software. The discussion highlights the dependence on the definitions and settings within Mathcad, as well as the unresolved nature of the mathematical treatment of indeterminate forms.

Nikitin
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I was doing some homework, trying to solve an equation by using algebra instead of reading from a graph (like I was supposed to), and I stumbled upon something:

Check out the attachment.

Why does the graph of f(x)=x/x have a T shape, with the vertical line starting at x=0 ? I know the graph isn't kind-of supposed to be defined for x=0, but I can't explain this anyway.
 

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Hi Nikitin! :smile:
Nikitin said:
… I know the graph isn't kind-of supposed to be defined for x=0, but I can't explain this anyway.

It should just have a tiny hole at x = 0,

since, as you say, it isn't defined there.​

I expect that particular graphing site (which one is it?) has a special way of dealing with 0/0 …

it looks like it's putting it equal to 0 …

so it joins that point, (0,0), to the rest of the graph by a line. :smile:​
 
I'm using mathcad. great program.

anyway, I think it's supposed to be like this.. I used this function A=[(x-1)(x-2)^2 +4]/x which had a similar line going vertically from y=0 to y=8.
The line actually represented that for x=0 A could be whatever from 0 to 8, and that actually made sense and was correct. I know my situation is terribly explained, but point is I think the line is supposed to be there.
 
Nikitin said:
I know my situation is terribly explained, but point is I think the line is supposed to be there.

What Tiny Tim said.

You shouldn't "believe" anything that is generated by a computer program, unless you understand why it's right or wrong.

Whatever MathCad is doing here, even if it's reinforcing your personal opinion about how math is "supposed to be", that isn't helping you learn what's right.
 
well it's not my personal opinion, if the function in post 3# wouldn't have gone with the vertical line then my answer would be incorrect.
 
Nikitin said:
anyway, I think it's supposed to be like this.. I used this function A=[(x-1)(x-2)^2 +4]/x which had a similar line going vertically from y=0 to y=8.
The line actually represented that for x=0 A could be whatever from 0 to 8, and that actually made sense and was correct. I know my situation is terribly explained, but point is I think the line is supposed to be there.

A is undefined when x = 0. There should NOT be a vertical line.

Your function A is identical to y = x2 - 5x + 8, except that there is a "hole" in the graph of A at the point (0, 8). The graph of y = x2 - 5x + 8 is a parabola that opens up.

Nikitin said:
well it's not my personal opinion, if the function in post 3# wouldn't have gone with the vertical line then my answer would be incorrect.
 
tiny-tim said:
Hi Nikitin! :smile:


It should just have a tiny hole at x = 0,

since, as you say, it isn't defined there.​

I expect that particular graphing site (which one is it?) has a special way of dealing with 0/0 …

it looks like it's putting it equal to 0 …

so it joins that point, (0,0), to the rest of the graph by a line. :smile:​

By default, Mathcad defines 0/0 as 0. There is an option to turn it off, thus allowing the user to catch the error and deal with it according to the nature of the problem.

NR

from the main menu:
Tools \ Worksheet Options ...​
This brings a dialog box with several tabs, choose the 'Calculation' tab and clear the '0/0=0' checkbox.
 
NemoReally said:
By default, Mathcad defines 0/0 as 0. There is an option to turn it off …

ahh!

thanks, NemoReally :smile:​
 
However, it is very likely that "round off error" for numbers very close to 0 will cause difficutly with things like f(x)/g(x) where f(x) and g(x) are very close to 0 themselves.
 

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