#What graph is this?

18 messages · Page 1 of 1 (latest)

stoic fulcrum
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As in what's the cartesian format. I suspect a rational polynomial but can't find it.

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quartz mountainBOT
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regal kayak
# stoic fulcrum As in what's the cartesian format. I suspect a rational polynomial but can't fin...

Well, it does look like a rational function. Here are some things we can notice about it.

  1. Its degree is odd.
  2. Degree of the numerator is smaller than the degree of the denominator.
  3. The leading coefficients of the numerator and denominator have different signs.
  4. It has a root x = 0 of even multiplicity.
  5. It has two poles: one at x = -1 or so of even multiplicity and one at x = 2 of odd multiplicity.
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Actually, it also seems to either be undefined for (-2, -1), or so negative that we can't see it.

stoic fulcrum
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I assume it's asymptotic at those points since it seems to be a rational function

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I don't really know where to approach except from trying values

regal kayak
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Well, it does somewhat look like -x^2/((x + 1)(x^2 - 4)).

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Ah, wait, no.

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Corrected.

stoic fulcrum
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Yeah - the problem is always either there's too much segments or the segments are on the wrong side of the y axis.

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regal kayak
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Considering that we seem to have f(1) = 1, I think multiplying it by 6 will give an even better result.

regal kayak
stoic fulcrum
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oh wait fair enough thats very close

regal kayak
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I think the function should be pretty close to -6x^2/((x + 1)(x^2 - 4)).

stoic fulcrum
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It seems to be slightly off in the sense that f(-5) is shown to be below 1 , but in the graph it evaluates to a number above 1

image.png
regal kayak
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Hm... Well, we can tinker with multiplicities a bit more, but we can't really do anything else without the values.

stoic fulcrum
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+close