What does the transformation f(x)↦8f(x) do to the graph of f(x)?



The transformation \( f(x) \mapsto 8f(x) \) applies a **vertical stretch** to the graph of \( f(x) \).

### Effect:
- **Vertical Stretch**: The factor of 8 means that every y-coordinate on the graph of \( f(x) \) is multiplied by 8. As a result, the graph becomes taller, stretching vertically by a factor of 8. 

### Key Points:
- Points on the x-axis (where \( f(x) = 0 \)) remain unchanged.
- Points above the x-axis are moved further away from the x-axis.
- Points below the x-axis are also moved further away from the x-axis, but in the negative direction.

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Do you want details or have any questions? Here are some related questions:

1. What happens to the graph if the transformation is \( f(x) \mapsto \frac{1}{2}f(x) \)?
2. How would the graph change if the transformation was \( f(x) \mapsto -8f(x) \)?
3. What does the transformation \( f(x) \mapsto f(2x) \) do to the graph?
4. How does the transformation \( f(x) \mapsto f(-x) \) affect the graph?
5. What happens if you apply the transformation \( f(x) \mapsto f(x+2) \)?
6. How would the graph change with \( f(x) \mapsto 8f(x-3) \)?
7. What does the transformation \( f(x) \mapsto 8f(-x) \) do to the graph?
8. What effect does the transformation \( f(x) \mapsto 8f(x) + 5 \) have on the graph?

**Tip**: Multiplying a function by a constant greater than 1 stretches the graph vertically, while a constant between 0 and 1 compresses it.

Explore the transformation f(x) ↦ 8f(x) in function graphs. Understand how this vertical stretch affects the graph, including key points such as unchanged x-axis points and vertical scaling by a factor of 8. Suitable for advanced high school students and anyone interested in function transformations.

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