To determine the transformation of the graph of \( f(x) = \sin x + 2 \) to the graph labeled as Option 2, we need to analyze the options and transformations that could have occurred.
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Vertical Shifts: The function \( f(x) = \sin x + 2 \) has a vertical shift upwards by 2 units. If the transformation involved a vertical shift downwards, we could be looking at \( f(x) = \sin x \) or something similar.
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Reflections:
- \( f(-x) \): This reflects the graph over the y-axis.
- \( -f(x) \): This reflects the graph over the x-axis.
- \( -f(-x) \): This reflects over both axes.
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Horizontal Shifts: The function \( f(x - 7) \) would shift the graph horizontally.
Given the options, to match with what option 2 represents, we need to examine:
- If the graph appears inverted, then it is based on \(-f(x)\) or \(-f(-x)\).
- If the graph looks like the original sine wave but is shifted or reflected, we can look into \( f(-x) \) or \( f(x - 7) \).
To conclude correctly: If Option 2 is indeed an upside-down version of \( f(x) \), then Option 2 would best match with \( -f(x) \). If it shows a reflection along with a shift, we need to clarify more based on the specific appearance of Option 2.
Without the image, I cannot confirm the exact transformation. However, based on the descriptions provided, if Option 2 represents a graph that is vertically inverted, the best response would be:
Option 2 is the graph of \( -f(x) \).
If the graph reflects across the y-axis or involves any horizontal transformations or further shifts, the respective options would vary accordingly.