# Syntax for multivariable functions

tpgettys shared this question 1 year ago

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? 1

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 1

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. 1

Hi tpgettys!

I understand your point and now the famous .... but ;-)

There is a difference between e. g. f(x)=x² and y=x².

The second one is a conic and you have to use this form to have the conic-commands available.

I realize the difference here in Simonas reply: https://help.geogebra.org/topic/tangente-wird-nicht-richtig-gelegt

and the difference is a little bit hidden in this section: https://wiki.geogebra.org/e...

You may enter a conic section as a quadratic equation in x and y.

And I think that's why e. g. f(y)=2*y is forbidden, but x=2*y and f(s)=2*s are allowed (the lines are different).

Hope that helps you and kind regards

mire2  1  1

another solution:

`Reflect(x² + y², y = z)`