How to plot below multivalued function

[the cyclist]

What does the notation [0,x/4] mean here. Does that mean in the range x in [0,1], there is one function that has constant value 0, and another function has value x/4?

[HEMANT K NASHINE]

The function T is multivalued. Meaning of multivalued is : for one input T will have more than one output. Examples for given function : In [0,1]. For x=0, Tx =_0 x=1, Tx =[0,1/4] means all values lies between 0 and 1/4 means there are infinitely many values. Similarly for any other values between 0 and 1, Tx is defined like this. For x=1/2, Tx =[0,1/8] means all values between 0 and 1/8. Similarly we can find T for interval (1, infinity). I want graph for such function. Please help.

Answer 1

[John D'Errico]

But it is not a function, in some standard mathematical sense of the word.

https://en.wikipedia.org/wiki/Function_(mathematics)

In there, we read "In mathematics, a function[note 1] is a relation between sets that associates to every element of a first set exactly one element of the second set."

You have some general mapping that takes an input number, and produces a set of results for any input. I don't know how complicated the output set might be, because your example is surely just an example. People rarely ever actually post what they really want to plot, instead making up some trivial example.

In the case of the problem you posed, I would just determine the set of outputs as a polygonal region, then use a tool like patch or fill to plot it.

For example, here on the interval [0,1], the region to be plotted is a simple triangle. For x > 1, the region is one that has one straight edge, and another curved one, but it is trivial to generate a polygon that will be sufficiently smooth.

Note that the boundary, at x==1 is important, because computers cannot handle strict inequalities well, especially for just a plot. You you would plot that region for x on an interval like [0,5], perhaps. If you go out too far, then you will not see the tiny triangle between 0 and 1 in the plot. Regardless, the result will be trivial to create, and it is completely your choice how far out you will go.

Why you want to do this is purely up to you. But the plot itself is trivial to build.

Answer 2

[HEMANT K NASHINE]

The function is correct . And what you taking Or given in Wikipedia that is for single valued function and my function is more general than single valued as you later mentioned as polygon or a line corresponding to each input. As I’m beginner, I don’t how to plot this type of function. I would be thankful if you provide me code for this. Thanks and regards