To graph the function $f(x) = -x^3$, we select $x$-values, apply the function to find the corresponding $y$-values, and plot the resulting ordered pairs. For example, using the $x$-values $-2$, $-1$, $0$, $1$, and $2$ produces the corresponding $y$-values $8$, $1$, $0$, $-1$, and $-8$. By plotting the points $(-2, 8)$, $(-1, 1)$, $(0, 0)$, $(1, -1)$, and $(2, -8)$ on a rectangular coordinate system and connecting them, we form the required downward-sloping curve.