What does the transformation f(x)↦4f(x) do to the graph of f(x)?

The transformation \( f(x) \mapsto 4f(x) \) scales the graph of \( f(x) \) vertically by a factor of 4.

### Explanation:
- Every point on the graph of \( f(x) \) has its \( y \)-coordinate multiplied by 4.
- This means that if a point on the graph of \( f(x) \) was originally at \( (x, f(x)) \), it will now move to \( (x, 4f(x)) \).
- The graph stretches away from the \( x \)-axis if \( f(x) \) is positive, and it stretches downward (further from the \( x \)-axis) if \( f(x) \) is negative.

### Effect:
- Vertical stretching by a factor of 4.
- No change to the \( x \)-coordinates or horizontal positioning.

Would you like more details or a visual explanation of this transformation?

Here are 5 related questions:
1. What does the transformation \( f(x) \mapsto \frac{1}{2}f(x) \) do to the graph?
2. How does \( f(x) \mapsto f(2x) \) affect the graph of \( f(x) \)?
3. What happens if you apply \( f(x) \mapsto -f(x) \)?
4. How does a horizontal shift, such as \( f(x) \mapsto f(x-3) \), affect the graph?
5. Can you combine both horizontal and vertical transformations?

**Tip:** Always check if a transformation affects the graph vertically (affecting \( y \)) or horizontally (affecting \( x \)) when analyzing changes.

Discover how the transformation f(x)↦4f(x) affects the graph of a function. This problem explains the vertical stretching of a graph by a factor of 4, covering key concepts like function transformations and scaling. Suitable for students in Grades 9-11.

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