To determine which points must be included in the graph of $f^{-1}(x)$ (the inverse of the function $f(x)$), we use the fact that the inverse function swaps the $x$- and $y$-coordinates of each point on the graph of $f(x)$.

Given the points on $f(x)$:

• $(2, 3)$
• $(-5, 1)$
• $(10, -3)$

The points on the graph of $f^{-1}(x)$ will be:

• $(3, 2)$ (from $(2, 3)$)
• $(1, -5)$ (from $(-5, 1)$)
• $(-3, 10)$ (from $(10, -3)$)

Thus, the points that must be included in the graph of $f^{-1}(x)$ are:

• $(3, 2)$
• $(1, -5)$
• $(-3, 10)$

Would you like more details or have any questions? Here are five related questions you can explore:

1. How do you find the inverse of a function algebraically?
2. What are the conditions for a function to have an inverse?
3. How does the graph of $f^{-1}(x)$ compare to the graph of $f(x)$?
4. Can every function have an inverse? Why or why not?
5. How do you verify if two functions are inverses of each other?

Tip: When graphing inverse functions, the line $y = x$ serves as a mirror line for the reflection of points between the functions.