1. The problem asks to identify the graph that shows the inverse of the function $f(x)$, which is an increasing S-shaped curve passing through the origin. 2. The inverse function $f^{-1}(x)$ swaps the roles of $x$ and $y$ in $f(x)$, meaning the graph of $f^{-1}(x)$ is the reflection of the graph of $f(x)$ across the line $y=x$. 3. Since $f(x)$ is an increasing S-shaped curve passing through the origin, its inverse will also be an increasing S-shaped curve passing through the origin but reflected over the line $y=x$. 4. To verify, if $f(x)$ passes through $(a,b)$, then $f^{-1}(x)$ passes through $(b,a)$. 5. Therefore, the graph showing the inverse of $f(x)$ is the reflection of the original S-shaped curve across the line $y=x$. Final answer: The inverse graph is the reflection of the original S-shaped curve across the line $y=x$.