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The question asks to manipulate the graph of the function \( f(x) \) in three different ways: 

1. **\( f(-x) \)**: This represents a reflection of the graph of \( f(x) \) across the **y-axis**. To draw this, flip the graph horizontally. For example, a point \( (a, b) \) on the original graph will become \( (-a, b) \) on the new graph.

2. **\( -f(x) \)**: This represents a reflection of the graph of \( f(x) \) across the **x-axis**. To draw this, flip the graph vertically. A point \( (a, b) \) on the original graph will become \( (a, -b) \) on the new graph.

3. **\( -f(-x) \)**: This combines both transformations: first reflect the graph horizontally across the **y-axis** (giving \( f(-x) \)), and then reflect that result vertically across the **x-axis** (giving \( -f(-x) \)).

Let's now break it down:

### Original graph of \( f(x) \):
- There is a downward curve from \( (-3, 4) \) to \( (0, 0) \).
- A small line segment from \( (0, 0) \) to \( (1, 1) \).
- An open circle at \( (1, 2) \) followed by a horizontal line from \( (1, 3) \) to \( (2, 3) \).
- An upward line starting from an open circle at \( (2, 3) \) and passing through \( (3, 4) \).

### a) \( f(-x) \):
- Reflect the graph across the **y-axis**. For example:
  - \( (-3, 4) \) becomes \( (3, 4) \),
  - \( (0, 0) \) stays the same,
  - \( (1, 1) \) becomes \( (-1, 1) \),
  - The rest follows similarly.

### b) \( -f(x) \):
- Reflect the graph across the **x-axis**. For example:
  - \( (-3, 4) \) becomes \( (-3, -4) \),
  - \( (0, 0) \) stays the same,
  - \( (1, 1) \) becomes \( (1, -1) \),
  - And so on.

### c) \( -f(-x) \):
- First reflect the graph across the **y-axis** (as in part a), and then reflect the result across the **x-axis**. For example:
  - \( (-3, 4) \) becomes \( (3, 4) \) (after reflecting across y-axis), and then \( (3, -4) \) after reflecting across x-axis.
  - Continue similarly for the rest of the graph.

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Do you want me to create the graphs for each transformation?

### Follow-up Questions:
1. What general effect does \( f(-x) \) have on a graph?
2. How does the transformation \( -f(x) \) change the shape of a function graphically?
3. Can you combine multiple transformations like \( -f(-x) \)? How?
4. How can the domain and range change when applying transformations like these?
5. What are the coordinates of key points after applying \( -f(x) \) to your graph?

**Tip**: When transforming functions, always reflect points individually to ensure accuracy.

Given f(x), draw the following: a) f(-x), b) -f(x), c) -f(-x).

Explore how to draw the transformations of f(x), including f(-x), -f(x), and -f(-x). This guide covers reflections across the y-axis, x-axis, and both axes. Suitable for high school students learning function transformations.

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