How would I hand-graph a region that is bounded by $z = 6 - 2 x^2/3, x = y^2$, and the $xy$-plane?
2026-03-28 13:49:57.1774705797
Graphing 3D function
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Put $y$ and $z$ as a function of the single variable $x$, i.e.,
$y(x) = \sqrt{x}$
$z(x) = 6 - \frac{2 x^2}{3}$
and then compute three-dimensional coordinates $\{ x, y(x), z(x) \}$ for a range of $x$.
If you're working in the stone age and need to do this by hand, make a table with values of $x$, $y$, $z$ and plot them in three dimensions and connect them by a smooth curve.
But why oh why do this by hand?!