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Given the graph of y equals f left parenthesis x right parenthesis as shown below, sketch the graph of y equals open vertical bar f left parenthesis x right parenthesis close vertical bar.

The graph you provided appears to represent a function with a "V" shape, similar to an absolute value function, \( f(x) \), with three key points at \((-4, 0)\), \((4, 0)\), and \((0, -8)\).

To sketch the graph of \( y = |f(x)| \), we make the following observations:

1. **Positive Values of \( f(x) \)**: Any points where \( f(x) \geq 0 \) (i.e., points above or on the x-axis) will remain unchanged since the absolute value of a non-negative number is itself.
   
2. **Negative Values of \( f(x) \)**: Any points where \( f(x) < 0 \) (i.e., points below the x-axis) will reflect across the x-axis, turning those values positive. This means that any parts of the graph below the x-axis will be mirrored above the x-axis.

### How to sketch \( y = |f(x)| \):
- For the points on the graph that lie on or above the x-axis (like at \( (-4, 0) \), \( (4, 0) \)), those points remain the same.
- For the point at \( (0, -8) \), it will reflect across the x-axis to become \( (0, 8) \).

Thus, the portion of the graph below the x-axis will be "flipped" above it, while the portion already above or on the x-axis will remain unchanged.

Would you like a detailed sketch of the modified graph, or do you have any other questions? 

### Here are 5 related questions for further understanding:
1. What is the domain and range of the original function \( f(x) \) and its transformation \( |f(x)| \)?
2. How do we find the zeros of \( |f(x)| \)?
3. Can this method be applied to any type of function? Why or why not?
4. What other transformations can be performed on \( f(x) \) besides taking the absolute value?
5. How does the vertex of the function change when transforming \( f(x) \) to \( |f(x)| \)?

### Tip: When working with absolute value transformations, always pay close attention to how negative values of the function change, as they reflect symmetrically across the x-axis.

Given the graph of y = f(x) as shown below, sketch the graph of y = |f(x)|.

Understand how to sketch the graph of the absolute value function y = |f(x)| based on the given graph of y = f(x). Learn about positive and negative values, reflection, and graph transformations. Suitable for students in Grades 8-10.

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