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

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SUMMARY

The discussion clarifies that in the Cartesian plane, the function z=f(x,y) is represented with z on the vertical axis and x, y on the horizontal axes. This representation is standard and will not be altered unless explicitly stated. The relationship between the variables is consistent, allowing for a clear association of x, y, and z as their respective coordinates. The function z=f(x,y) serves as an extension of the single-variable function y=f(x) to accommodate two variables.

PREREQUISITES
  • Understanding of Cartesian coordinates
  • Familiarity with functions of multiple variables
  • Basic knowledge of graphing techniques
  • Concept of height functions in three-dimensional space
NEXT STEPS
  • Study the concept of multivariable calculus
  • Learn about 3D graphing tools such as GeoGebra
  • Explore the implications of partial derivatives in functions of two variables
  • Investigate applications of z=f(x,y) in real-world scenarios
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Students and educators in mathematics, particularly those focusing on calculus and graphing, as well as professionals working with multivariable functions in engineering or data analysis.

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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?
 
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PhysicsHelp12 said:
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.
 

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