To determine which graph represents $y = f^{-1}(x)$, we need to understand a key property of an inverse function: the graph of $y = f^{-1}(x)$ is a reflection of $y = f(x)$ across the line $y = x$.

Given Graph of $f$:

• The function $f$ passes through points:
  • $(-2, -1)$
  • $(0, 0)$
  • $(2, 1)$

These key points can help identify the inverse function. When reflecting across $y = x$, the $(x, y)$ points of $f$ become $(y, x)$ for $f^{-1}$.

Reflection of Points:

1. $(-2, -1) \rightarrow (-1, -2)$
2. $(0, 0) \rightarrow (0, 0)$ (remains unchanged)
3. $(2, 1) \rightarrow (1, 2)$

We now look at the options to find the graph that contains these points:
$(-1, -2), (0, 0), (1, 2)$.

Analyzing the Options:

• Option A: Incorrect — does not match the reflected points.
• Option B: Correct — contains points $(-1, -2), (0, 0), (1, 2)$, consistent with the reflection.
• Option C: Incorrect — does not contain the correct reflected points.
• Option D: Incorrect — does not match the required reflected behavior.

Final Answer:

The correct graph of $y = f^{-1}(x)$ is Option B.

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Here are 5 related questions for further exploration:

1. What is the general relationship between $f$ and $f^{-1}$?
2. How do you verify if two functions are inverses of each other?
3. What is the graphical significance of the line $y = x$ in reflections?
4. How do you algebraically find the inverse of a function $f(x)$?
5. Why does the inverse of a function $f$ require $f$ to be one-to-one?

Tip: When analyzing inverses, always identify key points and reflect them across $y = x$.