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You are asked to match two functions, \( f(x) = |\sin(x)| \) and \( f(x) = \sin(|x|) \), with their corresponding graphs. Here's the breakdown of the two functions:

1. **\( f(x) = |\sin(x)| \)**: 
   - This graph will have the same shape as the sine function, but all the negative parts of the sine wave will be reflected above the x-axis, making all values non-negative.
   
2. **\( f(x) = \sin(|x|) \)**:
   - This function is the sine of the absolute value of \(x\), meaning it mirrors the sine wave around the y-axis. For negative values of \(x\), it will behave as if \(x\) were positive.

Now let's compare the graphs:
- **Left graph**: The sine wave looks mirrored around the x-axis, with all negative values made positive. This matches the behavior of \( f(x) = |\sin(x)| \).
  
- **Right graph**: The graph is symmetric around the y-axis, which is the characteristic of \( f(x) = \sin(|x|) \).

### Conclusion:
- **Left graph** corresponds to \( f(x) = |\sin(x)| \).
- **Right graph** corresponds to \( f(x) = \sin(|x|) \).

Would you like further details on these functions or any follow-up questions?

Here are 5 related questions to expand your understanding:
1. How does the graph of \( f(x) = \sin(x) \) differ from \( f(x) = |\sin(x)| \)?
2. What is the period of \( f(x) = \sin(|x|) \)?
3. How would you graph \( f(x) = \cos(|x|) \)?
4. What happens to \( f(x) = \sin(x) \) when the absolute value is applied to both \(x\) and \( \sin(x) \)?
5. Can you explain how symmetry around the x-axis and y-axis affects the graph?

**Tip**: When analyzing absolute value functions, observe how they alter both the negative and positive portions of a graph, reflecting or mirroring different parts.

Combine the functions f(x) = |sin(x)| and f(x) = sin(|x|) with their corresponding graphs.

Understand how to match f(x) = |sin(x)| and f(x) = sin(|x|) to their corresponding graphs. This problem covers concepts of trigonometric and absolute value functions, as well as symmetry and graph transformations.

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