What does the transformation f(x)↦f(x+8)–7 do to the graph of f(x)?

The transformation \( f(x) \mapsto f(x+8) - 7 \) involves two steps applied to the graph of the original function \( f(x) \):

1. **Horizontal Shift**: The term \( f(x + 8) \) indicates a shift of the graph of \( f(x) \) **8 units to the left**. This is because adding 8 inside the function argument \( x \) moves the graph in the opposite direction along the x-axis.

2. **Vertical Shift**: The term \( -7 \) indicates a shift of the graph **7 units down**. This is a direct translation along the y-axis.

In summary, the transformation \( f(x) \mapsto f(x+8) - 7 \) shifts the graph of \( f(x) \) **8 units to the left** and **7 units down**.

Would you like further details or have any questions on this transformation?

### Related Questions:
1. What would the transformation \( f(x) \mapsto f(x - 3) + 5 \) do to the graph?
2. How does the graph change with the transformation \( f(x) \mapsto -f(x) \)?
3. What effect does multiplying \( f(x) \) by a constant have on its graph?
4. How would the graph of \( f(x) \mapsto f(2x) \) be affected?
5. How does the transformation \( f(x) \mapsto f(x) + c \) generally affect the graph of \( f(x) \)?

**Tip**: When dealing with transformations, always remember that changes inside the function argument \( f(x + a) \) affect horizontal shifts, and changes outside, like \( f(x) + b \), affect vertical shifts.

Explore how the transformation f(x) ↦ f(x+8)–7 affects the graph of a function. Learn about horizontal and vertical shifts in graph transformations, shifting the graph 8 units to the left and 7 units down. Suitable for students in Grades 9-11.

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