Syntax for multivariable functions

tpgettys shared this question 3 years ago

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When I enter b(x, y) = x² + y² into the input line I see a paraboloid around the z-axis, and it is classified as a Multivariable Function. However, I get identical graphs when I enter

c(x, z) = x² + z² and d(y, z) = y² + z².

I expected to get paraboloids around each of the axes but that is not the case. Why is this?

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Comments (5)

mire2 ● 3 years ago

Hi tpgettys!

I think that the name of the two variables are always interpreted as x- and y-value.

If you type f(a,b)=a²+b² you will get the same picture, because the first variable a is dedicated to x and the second b is dedicated to y and so the function-value is always dedicated to z.

So if you want to have a paraboloid around the y-axis you can use the surface-command

Surface(u, u² + v², v, u, -10, 10, v, -10, 10)

note that x, y, z are not allowed as variables, but I think, they rename it internal if you use them: https://wiki.geogebra.org/e...

or an equation like

y-x²-z²=0

Kind regards

mire2

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tpgettys ● 3 years ago

Hi mire2, and thanks for your reply.

I understand that x, y and z are not allowed in the Surface() command, which seems to suggest that those letters are dedicated to specific usage.

In the 2D window if you enter f(y)=2*y you will get an error; x just be used for the independent variable. This difference should be documented somewhere, as it a source of great confusion (at least in my mind!), but I have not run across it yet.

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