How Does the Cartesian Plane Represent Functions Like z=f(x,y)?

[PhysicsHelp12]

y=f(x) to z=f(x,y) ? Help

My question is :


when z=f(x,y) is written down ...

it's assume that we're working in the cartesian plane with z on the

vertical axis, x and y on the horizontal right?


And they're not going to mix that around on me unless otherwise

stated?


So I can associate the variables x and y and z in my head --as

meaning the x y and z coordinate respectively ...and theyren not

going to have x be the 'y' coordinate on the graph and x be the 'z'

coordinate...?




z=f(x,y) is the y=f(x) of 2 variables?

 

[Defennder]

My question is :

when z=f(x,y) is written down ...

it's assume that we're working in the cartesian plane with z on the

vertical axis, x and y on the horizontal right?

Yes, that's usually how it's pictured.

And they're not going to mix that around on me unless otherwise

stated?

So I can associate the variables x and y and z in my head --as

meaning the x y and z coordinate respectively ...and theyren not

going to have x be the 'y' coordinate on the graph and x be the 'z'

coordinate...?

If it's expressed in the form z=f(x,y), you can think of z graph as being height function of the solid.

z=f(x,y) is the y=f(x) of 2 variables?

Yes.