Is there possible way to draw function $\vec{f}: R^2 \to R^2 $ such as like $\vec{f}(x,y) = \sin x+ \sin y, y+\sin x\ $ and other $\vec{f}(x,y)$ in $xy$-corordinate instead of $xyz$ plane. Is it okay to do it on some online graphers like symbolab and desmos? Thank a lot!
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$\begingroup$Strictly speaking it's not possible without loss of information: You need 2 dimensions for the Domain (the pairs $(x,y)$ and 2 dimensions for the image (the pairs $(f_1(x,y),f_2(x,y))$, that means 4 dimensions.
For plotting (and in general ;)) you have 3 dimensions at best. A workaround would be to plot $f_1(x,y)$ and $f_2(x,y)$ separately (e.g. ).
You can also plot the absolute value $|f(x,y)|$:
One could use colours as an additional "dimension", but I've only seen this with complex functions ${\displaystyle f:\mathbb {C} \to \mathbb {C} }$: . It helps in complex analysis and you are down to the xy-Plane, but otherwise it might not be helpful.
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