To describe the transformation from [tex]\( f(x) = \sin(x) \)[/tex] to [tex]\( g(x) = \sin(x) - 17 \)[/tex], let’s analyze the function transformation step by step:
1. Identify the transformation: We start with the original function [tex]\( f(x) = \sin(x) \)[/tex] and we want to understand how it turns into [tex]\( g(x) = \sin(x) - 17 \)[/tex].
2. Understand the effect of subtraction: The transformation involves subtracting 17 from the original function. This operation affects the vertical position of the graph.
3. Vertical shift: When a constant is subtracted from a function, it results in a vertical shift. Specifically:
- If you subtract a positive number, the graph of the function moves downward.
- Conversely, if you add a positive number, the graph moves upward.
4. Apply the transformation: Considering [tex]\( g(x) = \sin(x) - 17 \)[/tex]:
- The entire graph of [tex]\( \sin(x) \)[/tex] is shifted downward by 17 units.
Thus, the correct description of the transformation from [tex]\( f(x) = \sin(x) \)[/tex] to [tex]\( g(x) = \sin(x) - 17 \)[/tex] is that [tex]\( f(x) \)[/tex] is shifted 17 units down.
Therefore, the correct answer is:
B. [tex]\( f(x) \)[/tex] is shifted 17 units down to [tex]\( g(x) \)[/tex].
