To determine the domain and range of the inverse function $f^{-1}(x)$ from the graph of $f(x)$, we need to remember that:

• The domain of $f^{-1}(x)$ is the range of $f(x)$.
• The range of $f^{-1}(x)$ is the domain of $f(x)$.

From the graph:

1. Domain of $f(x)$: The function starts at $x = -4$ and ends at $x = 6$. Hence, the domain of $f(x)$ is: $\text{Domain of } f(x) = [-4, 6]$

2. Range of $f(x)$: The function ranges vertically from $y = -4$ to $y = 6$. Hence, the range of $f(x)$ is: $\text{Range of } f(x) = [-4, 6]$

Thus, for the inverse function:

• Domain of $f^{-1}(x)$ (which is the range of $f(x)$) is: $\text{Domain of } f^{-1}(x) = [-4, 6]$

• Range of $f^{-1}(x)$ (which is the domain of $f(x)$) is: $\text{Range of } f^{-1}(x) = [-4, 6]$

These are the required answers in interval notation.

Let me know if you have any further questions or need additional details.

Here are five related questions:

1. How do you find the inverse of a function algebraically?
2. What are the conditions for a function to have an inverse?
3. Can the domain of a function ever include infinity?
4. What is the relationship between the graphs of a function and its inverse?
5. How would the graph of the inverse $f^{-1}(x)$ look based on the given function?

Tip: When switching between a function and its inverse, remember to swap the x and y values!