Question
Reflections About the Origin Quick Check
5 of 55 of 5 Items
Question
Use the image to answer the question.
Five labeled sinusoidal waves are plotted on a coordinate plane.
Describe the transformation of the graph of f(x)=sinx+2
to the graph labeled Option 2.
(1 point)
Responses
Option 2 is the graph of −f(x)
.
Option 2 is the graph of negative f times x.
Option 2 is the graph of f(x−7)
.
Option 2 is the graph of f of open paren x minus 7 close paren.
Option 2 is the graph of f(−x)
.
Option 2 is the graph of f of negative x.
Option 2 is the graph of −f(−x)
.
Option 2 is the graph of negative f times negative x.
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Answers
GPT-4o mini
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.
1. The function \( f(x) = \sin(x) + 2 \) represents a vertical shift of the sine function upward by 2 units.
2. 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. The function \( f(x) = \sin(x) + 2 \) represents a vertical shift of the sine function upward by 2 units.
2. 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.