To graph the inverse function based on the given graph, follow these steps:

1. Understand the Inverse Function Rule: An inverse function reflects across the line $y = x$. The coordinates of each point on the function $f(x)$ become $(y, x)$ for the inverse.

2. Find Key Points on the Graph: Identify distinct points on the original graph and swap their $x$- and $y$-coordinates. For example:

   • If a point on the graph is $(-6, 0)$, the inverse will include $(0, -6)$.
   • If a point is $(-2, 3)$, the inverse will include $(3, -2)$.
   • Continue this for all identifiable points.

3. Plot the Inverse Points: Use the new set of coordinates to plot the inverse function on the graph.

4. Draw a Smooth Curve: After plotting the points, connect them to form the curve of the inverse function.

5. Check Symmetry: Ensure the graph of the inverse function is symmetrical with respect to the line $y = x$ when compared with the original function.

Do you want me to assist you by plotting the points or verifying any part of this process?

Related Questions:

1. How do we determine if a function has an inverse?
2. Can every function have an inverse? Why or why not?
3. What is the importance of the line $y = x$ in graphing inverse functions?
4. How do domain and range change for a function and its inverse?
5. How do you algebraically verify if two functions are inverses of each other?

Tip:

Always ensure the original function passes the horizontal line test; otherwise, it might not have an inverse