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I'm looking for a proper word or words that would describe a function that would start at zero, gradually climb toward one and then abruptly curve into the infinity.

Like on the attached graph?enter image description here

Dimitri Vorontzov
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  • Welcome to Mathematics Stack Exchange. It has a vertical asymptote – J. W. Tanner Feb 21 '20 at 14:12
  • @J.W.Tanner Thank you! I googled "vertical asymptote" just now and it seems to be somewhat different from what I'm looking for: https://www.purplemath.com/modules/asymtote.htm Namely, it seems to be the opposite. What I need is something that's on the positive side of the graph, crawling near zero for a while and then abruptly curving upward... – Dimitri Vorontzov Feb 21 '20 at 14:16
  • Your graph looks like $y=\dfrac1 {x^2}$; a function could be positive or negative to the left of a vertical asymptote; cf. $y=\dfrac{-1}x$ and $y=\dfrac1x$ – J. W. Tanner Feb 21 '20 at 14:19
  • @J.W.Tanner Is there a name for it? Something like "cubical parabola" etc. Let me explain why I ask. I'm trying to find a clear mathematical description of the graph that would illustrate a sudden spike in a dramatic conflict in traditional Chinese storytelling... – Dimitri Vorontzov Feb 21 '20 at 14:23
  • @J.W.Tanner Changed my illustration to ask question in a less incoherent way. Could you please take a look? – Dimitri Vorontzov Feb 21 '20 at 14:33
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    $y=\dfrac1x$ is a hyperbola – J. W. Tanner Feb 21 '20 at 14:45
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    Why do you need a clear mathematical description for a purely figurative analogy? You could just say "exponentially rising" and then people won't have to crack open a math textbook just to figure out what you're trying to say about literature. –  Feb 21 '20 at 14:48
  • @J.W.Tanner a hyperbola is slightly closer, for example this one: https://www.geogebra.org/m/aStXWPwb – but it seems inverted. What would be non-inverted version? – Dimitri Vorontzov Feb 21 '20 at 15:45
  • @Rahul Thank you. The "why" is because explaining something with a clear math example is often the easiest. "Exponentially rising" could mean all kinds of things. but what I need to show is the dynamic not rising at all... until suddenly it abruptly curves up. Just like on the graph I posted. Surely there has to be a function that does just that? – Dimitri Vorontzov Feb 21 '20 at 15:47
  • @DimitriVorontzov: you mean like $y=\dfrac{-1}x$ ? – J. W. Tanner Feb 21 '20 at 15:52
  • @J.W.Tanner I think this may be the one. But I'm trying to run it here and it wouldn't show me the graph: https://www.desmos.com/calculator/ Could you help me please? What would it look like? – Dimitri Vorontzov Feb 21 '20 at 15:55
  • @J.W.Tanner I was able to check, and it places the curves differently from the graph I used. What I need is to place the curve in the positive: + x and + y... Sorry for torturing you with this! ;-) – Dimitri Vorontzov Feb 21 '20 at 15:58
  • Did you try $y=\dfrac1{x^2}$? – J. W. Tanner Feb 21 '20 at 16:01
  • @J.W.Tanner Same effect: the mirror image of what I'm looking for. :-( – Dimitri Vorontzov Feb 22 '20 at 19:45

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