It could be any shape - continuous or not, as long as any vertical line intersected it at most once.
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In general, it is impossible. You could try putting together a data set using as many of the points as possible from the graph. Then try various regressions. You may have to perform transformations on the data if the function rule is not straightforward. This could require some very high level statistical techniques. You could be lucky and the graph is a straight line!
the graph is called a line
A sine graph!
A cubic graph!
The Mandelbrot graph is generated iteratively and so is a function of a function of a function ... and in that sense it is a composite function.