Let's analyze the graph in your image to determine the inverse function values $f^{-1}(x)$.

From the graph, we can find $f^{-1}(x)$ by interpreting it as finding the x-value that corresponds to a given y-value on the graph of $f(x)$.

Here’s how to determine each:

1. $f^{-1}(-4)$: Find the point on the graph where $f(x) = -4$. The corresponding x-value is $f^{-1}(-4)$.
2. $f^{-1}(-3)$: Look for $f(x) = -3$, then find the corresponding x-value, which gives $f^{-1}(-3)$.
3. $f^{-1}(0)$: When $f(x) = 0$, find the corresponding x-value to get $f^{-1}(0)$.
4. $f^{-1}(2)$: For $f(x) = 2$, find the corresponding x-value, giving $f^{-1}(2)$.
5. $f^{-1}(4)$: Locate where $f(x) = 4$, and find the corresponding x-value, resulting in $f^{-1}(4)$.

Let me inspect the graph closely and determine these values.I've opened the image to analyze the graph more closely. Let's now determine the values for the inverse function $f^{-1}$.

From the graph:

1. $f(x) = -4$ corresponds to $x = -8$, so $f^{-1}(-4) = -8$.
2. $f(x) = -3$ corresponds to $x = -6$, so $f^{-1}(-3) = -6$.
3. $f(x) = 0$ corresponds to $x = -2$, so $f^{-1}(0) = -2$.
4. $f(x) = 2$ corresponds to $x = 1$, so $f^{-1}(2) = 1$.
5. $f(x) = 4$ corresponds to $x = 4$, so $f^{-1}(4) = 4$.

The answers are:

• $f^{-1}(-4) = -8$
• $f^{-1}(-3) = -6$
• $f^{-1}(0) = -2$
• $f^{-1}(2) = 1$
• $f^{-1}(4) = 4$

Would you like more details or explanations on how these values were determined?

Here are 5 related questions you might consider:

1. What is the graphical relationship between a function and its inverse?
2. How do you determine if a function is invertible from its graph?
3. Can all functions have inverses? Why or why not?
4. What does the graph of the inverse function $f^{-1}(x)$ look like compared to $f(x)$?
5. How can you algebraically find the inverse of a function?

Tip: The graph of a function and its inverse are reflections across the line $y = x$.