graph (of a multivariable function)

The set of points $(x,y,f(x,y))$ in space — a surface, one dimension bigger than a single-variable graph's curve.

The graph of $z=f(x,y)$ is the set of all points $(x,y,f(x,y))$ in $\mathbb{R}^3$ — one point directly above (or below) every $(x,y)$ in the domain, at a height equal to the output. A curve was the whole picture for a single-variable function; a surface is the whole picture here. Because a surface is too much to take in at once from every angle, the honest way to read one is to slice it into traces.

Examples

The graph of $z=4-x^2-y^2$ is a downward-opening paraboloid (a bowl) in space.