Graphing of functions

It’s pretty useful to visualise functions visually, especially for multivariable functions.

Multivariable functions

For multivariable functions, see:

• Trace
• Level curves and surfaces

When asked to graph a function, it’s a good idea to also graph the traces even if they don’t ask for it. We can graph in MATLAB and in Geogebra.

Cylinders

Sometimes we’re given a two-variable relation or function to graph: i.e., an ellipse defined only with $x$ and $y$. If $z$ isn’t specified, then the ellipse is valid for all $z\in \mathbb{R}$.

But if we’re given a domain restriction on $z$, i.e., $z\in [-2,2]$, then we cap the cylinder.