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I know that if $T$ is a single-valued mapping for example $T(x)=x^{2}$ for all $x\in[0,1]$ then its graph can be plot using

Plot[x^2, {x, 0, 1}]

Is there any way to plot a set-valued mapping like $Tx=[0,x]$ for all $x\in [0,1]$.? In (2D or in 3D)?

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1 Answer 1

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For example,the set-valued mapping $T x=[x^2,x^3]$,we can use ParametricPlot(or sometimes ParametricRegion)

ParametricPlot[{x, y}, {x, 0, 1}, {y, x^2, x^3}, 
 MeshFunctions -> {#1 &}, Mesh -> {{.6}}, MeshStyle -> Red]

enter image description here

Or

Plot[{x^2, x^3}, {x, 0, 1}, Filling -> {1 -> {2}}, AspectRatio -> Automatic]
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  • $\begingroup$ Thanks dear @cvgmt for your kind answar. I have a question can we plot its 3D graph in the case of my example $T=[0,x]$? $\endgroup$
    – Junaid
    Apr 14 at 22:48
  • $\begingroup$ @Junaid $x$ is two dimension? $\endgroup$
    – cvgmt
    Apr 14 at 22:53
  • $\begingroup$ Dear @cvgmt, no $x$ is a real number in the closed interval $[0,1]$. The is function maps $0$ 0n $\{0\}$, .....$0.5$ 0n $ [0,0.5]$ ,....., $1$ on $[0,1]$. $\endgroup$
    – Junaid
    Apr 14 at 22:55
  • $\begingroup$ @Junaid We need not use 3D. Just use 2D. ParametricPlot[{x, y}, {x, 0, 1}, {y, 0, x}, MeshFunctions -> {#1 &}, Mesh -> {{.6}}, MeshStyle -> Red] $\endgroup$
    – cvgmt
    Apr 14 at 22:59

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