To solve the inverse function values based on the given graph, let's analyze each requested $f^{-1}(x)$:

1. Understanding Inverse Functions: The inverse function $f^{-1}(y)$ finds the $x$-value that gives $y$ in the original function $f(x)$. In other words, for $f^{-1}(-4)$, we need to find $x$ such that $f(x) = -4$.

Step-by-Step Solutions

1. $f^{-1}(-4)$:

   • Locate $y = -4$ on the graph and find the corresponding $x$-value.
   • According to the graph, when $f(x) = -4$, $x \approx -2.5$.

   So, $f^{-1}(-4) \approx -2.5$.

2. $f^{-1}(-3)$:

   • Locate $y = -3$ on the graph and find the corresponding $x$-value.
   • Based on the graph, when $f(x) = -3$, $x \approx -1.5$.

   So, $f^{-1}(-3) \approx -1.5$.

3. $f^{-1}(0)$:

   • Locate $y = 0$ on the graph and find the corresponding $x$-value.
   • When $f(x) = 0$, $x \approx 0.5$.

   So, $f^{-1}(0) \approx 0.5$.

4. $f^{-1}(2)$:

   • Locate $y = 2$ on the graph and find the corresponding $x$-value.
   • When $f(x) = 2$, $x \approx 2.5$.

   So, $f^{-1}(2) \approx 2.5$.

Summary of Solutions

1. $f^{-1}(-4) \approx -2.5$
2. $f^{-1}(-3) \approx -1.5$
3. $f^{-1}(0) \approx 0.5$
4. $f^{-1}(2) \approx 2.5$

Would you like further details on how to interpret the inverse function from graphs?

Related Questions

1. What are the steps to find an inverse function algebraically?
2. How can we verify if two functions are inverses of each other?
3. How does the slope of the original function affect the inverse function?
4. What is the domain and range of an inverse function?
5. How do we handle cases where a function is not one-to-one?

Tip:

Remember, for a function to have an inverse, it must be one-to-one (pass the horizontal line test).