Sketch the graph and describe the vertical and horizontal traces.
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 . Take, for example, the
values . 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 .
Go to the site Functions of Two Variables to see how this function looks.
Tonio
Would the traces basically be:
Horizontal:
Vertical: