To find the inverse of the graph from the image, we need to create a table for the inverse function. An inverse of a function $f(x)$ essentially swaps the $x$- and $y$-coordinates of points on the original graph. Let's identify some key points from the graph and then switch their coordinates.

Step 1: Identifying Points on the Graph

Based on the graph, we can estimate a few points:

• $f(0) = 0$
• $f(1) \approx 1$
• $f(5) \approx 3$
• $f(10) \approx 5$
• $f(15) \approx 7$

Step 2: Creating the Table for $f^{-1}(x)$

To find the inverse, we swap the $x$- and $y$-coordinates of these points:

Step 3: Interpretation

The table shows the points for the inverse function $f^{-1}(x)$, where the roles of $x$ and $y$ are reversed.

Would you like further clarification on how the inverse is constructed, or do you want to explore specific properties of the function?

Related Questions:

1. How can you verify if two functions are inverses algebraically?
2. What are the key features of the inverse function from the graph?
3. What does it mean for a function to have an inverse?
4. How does the domain and range change for the inverse of a function?
5. Can every function have an inverse? If not, why?

Tip: To find the inverse graphically, you can reflect the original graph across the line $y = x$.