To sketch the graph of \( y = |f(x)| \), follow these steps:

1. **Start by sketching \( y = f(x) \)**: Plot the original function as if the absolute value wasn’t present.

2. **Identify the negative portions of \( f(x) \)**: Locate where the graph of \( y = f(x) \) is below the x-axis (i.e., where \( f(x) < 0 \)).

3. **Reflect the negative parts above the x-axis**: For any \( x \) where \( f(x) < 0 \), reflect the portion of the graph that is below the x-axis to make it positive. This means flipping it to the other side of the x-axis while maintaining its shape.

4. **Keep the positive parts unchanged**: For the regions where \( f(x) \geq 0 \), the graph remains as it is.

5. **Erase the parts below the x-axis**: After reflecting, remove any parts of the graph that remain below the x-axis, since \( |f(x)| \) is always non-negative.

### Example
If you have \( f(x) = x^2 - 4 \), first sketch \( f(x) = x^2 - 4 \), then reflect the part of the graph below the x-axis, and finally remove the portion that remains negative.

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Do you want to go into more detail or ask any questions about these steps?

Here are 5 related questions to deepen understanding:

1. What happens when the function \( f(x) \) is always positive?
2. How does the graph of \( |f(x)| \) change if \( f(x) \) is a linear function?
3. Can the graph of \( y = |f(x)| \) ever touch the x-axis?
4. What are some common mistakes to avoid when sketching \( y = |f(x)| \)?
5. How would the process differ for a piecewise function?

**Tip**: Always ensure the points where \( f(x) = 0 \) remain unchanged when sketching \( |f(x)| \).

Learn how to sketch the graph of y = |f(x)| by reflecting negative parts of the function above the x-axis. This guide explains step-by-step how to handle absolute value functions, covering key concepts like reflection and graphing techniques. Ideal for students in Grades 9-11.

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