To determine the correct transformation from \( f(x) = \sin x + 2 \) to the graph labeled as Option 2, we need to analyze the indicated transformations.
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\( f(x) = \sin x + 2 \): This is the basic sine wave shifted vertically upwards by 2 units.
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To understand the transformation represented by Option 2, we need to consider the options given:
- Option 2 is the graph of f(x−7): This would indicate a horizontal shift to the right by 7 units.
- Option 2 is the graph of f(x - 7): Same interpretation as above, indicating a right shift.
- Option 2 is the graph of −f(−x): This would reflect the graph across the y-axis and then reflect it across the x-axis.
- Option 2 is the graph of negative f times negative x: This statement is ambiguous and not standard notation.
- Option 2 is the graph of −f(x): This would reflect the graph across the x-axis.
- Option 2 is the graph of f(−x): This would reflect the graph across the y-axis.
To match the transformations visually, if Option 2 represents a basic sine graph that has only been shifted or reflected as described, we can look for changes indicating such transformations.
For a vertical shift, transformations such as (\( +2 \)) would not represent a new graph without changes to the horizontal aspects.
Knowing this, the option that likely describes a shift in the horizontal direction is Option 2 is the graph of f(x - 7) or phrased correctly, Option 2 is the graph of f(x−7).
Therefore, the best answer is:
Option 2 is the graph of f(x−7).
1 answer