The transformation described by \( f(x) \mapsto f(x - 6) - 4 \) involves two distinct operations on the graph of the function \( f(x) \):
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Horizontal Translation: The term \( f(x - 6) \) indicates a horizontal shift of the graph to the right by 6 units. This is because replacing \( x \) with \( x - 6 \) moves every point on the graph 6 units to the right.
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Vertical Translation: The term \( -4 \) indicates a vertical shift downward by 4 units. This means that after the horizontal shift, every point on the graph of \( f(x - 6) \) will then be moved down 4 units.
In summary:
- The overall transformation \( f(x) \mapsto f(x - 6) - 4 \) shifts the graph of \( f(x) \) 6 units to the right and 4 units down.
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