1. The problem is to draw the graph of the inverse function of a given function. 2. The inverse function, denoted as $f^{-1}(x)$, reverses the roles of inputs and outputs of the original function $f(x)$. If $f(a) = b$, then $f^{-1}(b) = a$. 3. To find the inverse function algebraically, swap $x$ and $y$ in the equation $y = f(x)$ and solve for $y$. 4. The graph of the inverse function is the reflection of the graph of the original function across the line $y = x$. 5. Important rule: The function must be one-to-one (pass the horizontal line test) to have an inverse that is also a function. 6. Steps to draw the inverse graph: - Plot the original function. - Draw the line $y = x$ as a reference. - Reflect each point of the original graph across the line $y = x$. - Connect these reflected points smoothly to form the inverse function graph. 7. Example: If $f(x) = 2x + 3$, then to find $f^{-1}(x)$: - Write $y = 2x + 3$. - Swap $x$ and $y$: $x = 2y + 3$. - Solve for $y$: $y = \frac{x - 3}{2}$. 8. The inverse function is $f^{-1}(x) = \frac{x - 3}{2}$. 9. The graph of $f^{-1}(x)$ is the reflection of $f(x)$ across $y = x$. Final answer: To draw the inverse function graph, reflect the original function's graph across the line $y = x$ after confirming the function is one-to-one and finding the inverse algebraically if needed.