# Thread: How do I graph a multivariable function?

1. ## How do I graph a multivariable function?

Sketch the graph and describe the vertical and horizontal traces.
$f(x,y) = y^2$

Is this simply a parabola that touches ONLY the yz-plane in R^3?
Would the traces basically be:
Horizontal:
$\pm\sqrt{c} = y } when z = c$

Vertical:
$z = y^2 \} when x = a$
$z = b^2 \} when y = b$

2. Originally Posted by ZeroVector
Sketch the graph and describe the vertical and horizontal traces.
$f(x,y) = y^2$

Is this simply a parabola that touches ONLY the yz-plane in R^3?

It can't be a parabola since it is a 2-variables function and thus is a surface in $\mathbb{R}^3$. Take, for example, the

values $f(0,y)$. Here, you get the usual parabola on the yz plane...but it is THE SAME for ANY value of x, so you actually get

a paraboloid every perpendicular to the xy-plane cut of which looks at the well-known parabola $x=y^2$.

Go to the site Functions of Two Variables to see how this function looks.

Tonio

Would the traces basically be:
Horizontal:
$\pm\sqrt{c} = y } when z = c$

Vertical:
$z = y^2 \} when x = a$
$z = b^2 \} when y = b$
.