# How to plot a set-valued mapping graph

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)?

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] Or

Plot[{x^2, x^3}, {x, 0, 1}, Filling -> {1 -> {2}}, AspectRatio -> Automatic]

• Thanks dear @cvgmt for your kind answar. I have a question can we plot its 3D graph in the case of my example $T=[0,x]$? Apr 14 at 22:48
• @Junaid $x$ is two dimension? Apr 14 at 22:53
• 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 $[0,1]$. Apr 14 at 22:55
• @Junaid We need not use 3D. Just use 2D. ParametricPlot[{x, y}, {x, 0, 1}, {y, 0, x}, MeshFunctions -> {#1 &}, Mesh -> {{.6}}, MeshStyle -> Red] Apr 14 at 22:59