# Why does this happen with my graph?

by Nikitin
Tags: graph, happen
 P: 619 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. Attached Thumbnails
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Hi Nikitin!
 Quote by Nikitin … 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.
 P: 619 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.
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Why does this happen with my graph?

 Quote by Nikitin 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.
 P: 619 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.
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 Quote by Nikitin 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.

 Quote by Nikitin 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.
P: 194
 Quote by tiny-tim Hi Nikitin! 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.
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