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The Gartner hype curve:

is a branded graphical presentation developed and used by American information technology (IT) research and advisory firm Gartner for representing the maturity, adoption and social application of specific technologies.

Source: https://en.wikipedia.org/wiki/Hype_cycle

And it looks like this:

enter image description here

Is there a function that can fit this curve? If not, what would be the closest approximation of the function that can fit this curve?

The first part of the curve looks like a gaussian/normal distribution and the second part looks like a partial quadratic function and the last partlooks like a right tail of the logarithm curve.

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There is no formally defined curve, just a picture. However, the picture suggests a curve that passes the vertical line test, and hence could be defined by a function. You could construct a simple function that looks like the picture with a generic curve-fitting method such as cubic splines.

I might add that this all seems like a pointless exercise because the hype cycle isn't a representation of any empirical data or mathematical object. It's just a picture that's drawn to look like a graph, presumably to mislead readers into thinking it's somehow scientific or quantitative. One might call it a fake graph.

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    $\begingroup$ Do you mind updating the post with R code to produce the plot? $\endgroup$
    – zx8754
    Dec 4, 2017 at 9:25
  • $\begingroup$ @zx8754 That's not really on-topic for this site. Try Stack Overflow. $\endgroup$ Dec 4, 2017 at 15:25
  • $\begingroup$ Agree, didn't want to duplicate the post, in case you had an R code ready. $\endgroup$
    – zx8754
    Dec 4, 2017 at 15:27

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