Transformation y =f(x)- 8 shifts the graph down 8 units

Yes, the transformation \( y = f(x) - 8 \) represents a vertical shift of the graph of the function \( f(x) \) **downward by 8 units**. This means that every point on the graph of \( f(x) \) is moved down by 8 units, but the shape and horizontal position of the graph remain unchanged.

### Explanation:
- In general, adding or subtracting a constant to a function affects the **vertical position** of its graph.
- If you have the function \( y = f(x) \), the transformation \( y = f(x) - 8 \) moves every point \( (x, f(x)) \) to the point \( (x, f(x) - 8) \).

This shift is often visualized as taking the graph of \( f(x) \) and dragging it downward along the y-axis by 8 units.

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### Relative Questions:
1. How does the transformation \( y = f(x) + 8 \) affect the graph?
2. What happens if you apply \( y = f(x + 8) \) instead of \( y = f(x) - 8 \)?
3. Can you combine vertical and horizontal shifts? If so, how would the graph change?
4. How does scaling (multiplying \( f(x) \) by a constant) affect the graph compared to shifting?
5. What other transformations could you apply to \( f(x) \) and what would their effects be?

### Tip:
For any vertical transformation of a graph, changes happen **outside** the function (like \( f(x) + k \)), while horizontal changes occur **inside** the function (like \( f(x + k) \)).

Transformation y = f(x) - 8 shifts the graph down 8 units

Understand the transformation y = f(x) - 8, where the graph of a function is shifted downward by 8 units. This concept explores vertical shifts of function graphs, with a clear explanation and suitable for students in Grades 9-12.

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