To find the values for $f^{-1}(x)$ using the graph of the function $f(x)$, we need to understand that the inverse function $f^{-1}(x)$ essentially swaps the roles of $x$ and $y$. In other words, if $f(a) = b$, then $f^{-1}(b) = a$.

Let's analyze the graph to answer each of the questions:

1. $f^{-1}(-4)$: We need to find the value of $x$ such that $f(x) = -4$.

   • From the graph, when $y = -4$, the corresponding $x$-value is approximately $x = 5$.
   • So, $f^{-1}(-4) = 5$.

2. $f^{-1}(-3)$: We need to find the value of $x$ such that $f(x) = -3$.

   • From the graph, when $y = -3$, the corresponding $x$-value is approximately $x = 4$.
   • So, $f^{-1}(-3) = 4$.

3. $f^{-1}(0)$: We need to find the value of $x$ such that $f(x) = 0$.

   • From the graph, when $y = 0$, the corresponding $x$-value is approximately $x = 1$.
   • So, $f^{-1}(0) = 1$.

4. $f^{-1}(2)$: We need to find the value of $x$ such that $f(x) = 2$.

   • From the graph, when $y = 2$, the corresponding $x$-value is approximately $x = -1$.
   • So, $f^{-1}(2) = -1$.

5. $f^{-1}(4)$: We need to find the value of $x$ such that $f(x) = 4$.

   • From the graph, when $y = 4$, the corresponding $x$-value is approximately $x = -3$.
   • So, $f^{-1}(4) = -3$.

To summarize:

1. $f^{-1}(-4) = 5$
2. $f^{-1}(-3) = 4$
3. $f^{-1}(0) = 1$
4. $f^{-1}(2) = -1$
5. $f^{-1}(4) = -3$

Would you like more details or have any questions about these calculations? Here are some related questions:

1. How do you find the inverse of a function algebraically?
2. What is the significance of the inverse function in real-world applications?
3. How can you graph the inverse of a function?
4. What are the conditions for a function to have an inverse?
5. How do you verify if two functions are inverses of each other?

Tip: When working with the inverse of a function, always check the original function's graph to ensure that the inverse values make sense within the given context.