1. The problem asks us to graph the inverse of the function $h$ given its graph with points $(-1,8)$, $(0,5)$, $(4,1.5)$, and $(6,1)$, but only for $x > 0$. 2. The inverse function $h^{-1}$ swaps the roles of $x$ and $y$. So each point $(a,b)$ on $h$ corresponds to $(b,a)$ on $h^{-1}$. 3. Since we only consider $x > 0$ for $h$, we only take points from $h$ where $x > 0$: $(0,5)$, $(4,1.5)$, and $(6,1)$. 4. Swap coordinates for these points to get points on $h^{-1}$: $(5,0)$, $(1.5,4)$, and $(1,6)$. 5. Plot these points on the blank coordinate grid for $h^{-1}$. 6. The inverse function graph will pass through these points and reflect the original graph across the line $y=x$. Final answer: The inverse function $h^{-1}$ has points approximately at $(5,0)$, $(1.5,4)$, and $(1,6)$ for $x > 0$.