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

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In summary, when z=f(x,y) is written down, it is usually assumed that we are working in the Cartesian plane with z on the vertical axis and x and y on the horizontal axis. The variables x and y represent the x and y coordinates respectively, and z represents the height function of the solid. This notation is similar to y=f(x) for two variables.
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PhysicsHelp12
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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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  • #2


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.
 

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

What is the difference between "Y=f(x)" and "z=f(x,y)"?

"Y=f(x)" is an equation that represents a single variable, Y, in terms of another variable, x. On the other hand, "z=f(x,y)" is an equation that represents a two-variable function, z, in terms of both x and y. In other words, "z=f(x,y)" takes into account the relationship between two variables, while "Y=f(x)" only considers the relationship between two variables.

How do you convert "Y=f(x)" to "z=f(x,y)"?

To convert "Y=f(x)" to "z=f(x,y)", you need to add the variable y to the equation. This can be done by either substituting y for a constant or another variable, or by multiplying y with a coefficient. For example, if Y=3x+2, then z=3x+2y or z=3x+2y+1 would be valid conversions.

What is the purpose of converting "Y=f(x)" to "z=f(x,y)"?

Converting from "Y=f(x)" to "z=f(x,y)" allows for a more comprehensive understanding of the relationship between variables. This can be particularly useful in scientific research, where multiple variables can have an impact on the outcome.

Can "Y=f(x)" and "z=f(x,y)" be solved simultaneously?

Yes, "Y=f(x)" and "z=f(x,y)" can be solved simultaneously by using the method of substitution or elimination. By solving for one variable in one equation and substituting it into the other equation, you can find the values for both variables.

How can "Y=f(x)" and "z=f(x,y)" be graphed?

"Y=f(x)" can be graphed on a two-dimensional coordinate plane, where the x-axis represents the independent variable, x, and the y-axis represents the dependent variable, Y. Similarly, "z=f(x,y)" can be graphed on a three-dimensional coordinate plane, where the x-axis represents x, the y-axis represents y, and the z-axis represents the dependent variable, z.

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