https://file.aiquickdraw.com/mathbot/file/1727319606043wd5tvzcp.jpg

The image provided shows a question based on the graph of a function \( f(x) \). To evaluate the answers, we can read the function values from the graph.

The points provided on the graph are:
- \( f(-3) = -9 \) 
- \( f(2) = 5 \)
- \( f(1) = 2 \)
- \( f^{-1}(1) = -2 \) (this is the x-value where \( f(x) = 1 \))
- \( f^{-1}(-3) = 3 \) (this is the x-value where \( f(x) = -3 \))

### Let's break it down:
1. **(a) \( f(-3) \)**: From the graph, when \( x = -3 \), \( f(-3) = -9 \).
2. **(b) \( f(2) \)**: From the graph, when \( x = 2 \), \( f(2) = 5 \).
3. **(c) \( f^{-1}(1) \)**: The inverse asks for the x-value when \( f(x) = 1 \), which is \( x = -2 \).
4. **(d) \( f^{-1}(-3) \)**: The inverse asks for the x-value when \( f(x) = -3 \), which is \( x = 3 \).

Now, you can proceed to fill in the answers for each part of the question:

- (a) \( f(-3) = -9 \)
- (b) \( f(2) = 5 \)
- (c) \( f^{-1}(1) = -2 \)
- (d) \( f^{-1}(-3) = 3 \)

Would you like more details on inverse functions or any other concept? 

Here are some related questions:
1. What is the graphical interpretation of an inverse function?
2. How can you verify if a function is one-to-one and thus invertible?
3. Can a function have an inverse if it is not one-to-one?
4. How does the horizontal line test help in determining invertibility?
5. What are some examples of real-world applications of inverse functions?

**Tip**: Inverse functions swap the input and output values of the original function, so visually, they reflect across the line \( y = x \).

Use the given graph of y = f(x) to evaluate the following: (a) f(-3), (b) f(2), (c) f^(-1)(1), (d) f^(-1)(-3).

Evaluate function and inverse function values using a given graph of y = f(x). Learn how to determine f(x) and f^(-1)(x) values from graphical points. Suitable for students in Grades 9-12.

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