To determine the correct description of the transformation of the graph of \( f(x) = \sin(x) + 2 \) to the graph labeled Option 2, we need to analyze the transformations involved.
- The function \( f(x) = \sin(x) + 2 \) represents a vertical shift of the sine function upward by 2 units.
- If Option 2 involves transformations, it could include vertical reflections, horizontal reflections, or shifts.
Here's a breakdown of the response options:
- Option 2 is the graph of −f(x): This would reflect the graph vertically (over the x-axis).
- Option 2 is the graph of negative f times x: This doesn't apply as it suggests a multiplication of the function rather than a reflection.
- Option 2 is the graph of f(x−7): This would represent a horizontal shift to the right by 7 units.
- Option 2 is the graph of f of open paren x minus 7 close paren: This is the same as the previous option and represents a horizontal shift to the right by 7 units.
- Option 2 is the graph of f(−x): This would reflect the graph over the y-axis.
- Option 2 is the graph of f of negative x: This is the same as the previous option and reflects the graph over the y-axis.
- Option 2 is the graph of −f(−x): This reflects the graph both vertically and horizontally.
Without seeing the actual image, the description that seems most likely is:
- If Option 2 reflects the graph vertically and/or horizontally, and based on typical transformations involving sine functions, it suggests that Option 2 is the graph of −f(−x).
You should refer to the image and the transformations displayed on Option 2 to make the final decision.
1 answer