The image shows a linear graph of a function $f(x)$, and the task is to draw the graph of its inverse function $f^{-1}(x)$.

Steps to graph the inverse of a function:

1. Reflect the graph over the line $y = x$: The graph of the inverse function is a reflection of the original function across the line $y = x$.
2. Swap the coordinates: For each point $(x, y)$ on the original graph, the corresponding point on the inverse graph will be $(y, x)$.

Graph details:

• The line passes through key points such as $(0, 0)$, $(1, 2)$, and $(2, 4)$.
• For the inverse, swap these points:
  • $(0, 0)$ remains unchanged.
  • $(1, 2)$ becomes $(2, 1)$.
  • $(2, 4)$ becomes $(4, 2)$.

Drawing the inverse:

• Plot the points $(0, 0)$, $(2, 1)$, $(4, 2)$, and extend the line accordingly.
• Ensure the line is symmetric about $y = x$.

Would you like further details or explanations?

Here are 5 related questions:

1. How do we verify if two functions are inverses of each other?
2. What is the general process for finding the inverse of a linear function algebraically?
3. How do inverse functions relate to one-to-one functions?
4. Can a function always have an inverse?
5. How does the domain and range of a function change when finding its inverse?

Tip: Always check if a function is one-to-one before finding its inverse; only one-to-one functions have inverses.