Question
Describe the transformation of the graph of f(x)=sinx+2 to the graph labeled Option 2.
(1 point)
Responses
A. Option 2 is the graph of −f(x)
B. Option 2 is the graph of −f(−x)
C. Option 2 is the graph of f(x−7)
D. Option 2 is the graph of f(−x)
(1 point)
Responses
A. Option 2 is the graph of −f(x)
B. Option 2 is the graph of −f(−x)
C. Option 2 is the graph of f(x−7)
D. Option 2 is the graph of f(−x)
Answers
Answered by
GPT-4o mini
To describe the transformation of the graph of \( f(x) = \sin(x) + 2 \) to the graph labeled Option 2, we should look for the specific transformations that match the options given.
1. **Option A: Option 2 is the graph of \( -f(x) \)**
This would reflect the graph of \( f(x) \) over the x-axis. The graph of \( -(\sin(x) + 2) \) would be \( -\sin(x) - 2 \), which shifts the graph down and flips it. This is not likely the transformation unless Option 2 shows a reflection over the x-axis.
2. **Option B: Option 2 is the graph of \( -f(-x) \)**
This transformation reflects the graph of \( f(x) \) over the y-axis and then flips it over the x-axis. This is a combination of transformations and would not just shift the graph vertically, so it's likely not the case unless Option 2 appropriately demonstrates these changes.
3. **Option C: Option 2 is the graph of \( f(x - 7) \)**
This would shift the graph of \( f(x) \) horizontally to the right by 7 units. Given the original function shifts the sine graph vertically up by 2, this option changes its horizontal position. If Option 2 does not demonstrate this horizontal shift, it isn't valid.
4. **Option D: Option 2 is the graph of \( f(-x) \)**
This transformation reflects the graph across the y-axis. For this option to be correct, we would see a mirror image of the graph of \( f(x) = \sin(x) + 2 \) on the left side of the y-axis.
Without the visual representation of Option 2, it's difficult to definitively choose the correct answer. However, consider the characteristics of the transformations involved:
- If Option 2 represents a vertical shift upwards or downwards without flipping or reflecting, then none of these options would apply.
- If it appears to be a horizontal shift to the right, option C would be correct, if it matches that description.
- If there are reflections involved, options A, B, or D may be designated based on the direction of the reflection.
In conclusion, please check the visual representation of Option 2 against the transformations described to choose the correct option.
1. **Option A: Option 2 is the graph of \( -f(x) \)**
This would reflect the graph of \( f(x) \) over the x-axis. The graph of \( -(\sin(x) + 2) \) would be \( -\sin(x) - 2 \), which shifts the graph down and flips it. This is not likely the transformation unless Option 2 shows a reflection over the x-axis.
2. **Option B: Option 2 is the graph of \( -f(-x) \)**
This transformation reflects the graph of \( f(x) \) over the y-axis and then flips it over the x-axis. This is a combination of transformations and would not just shift the graph vertically, so it's likely not the case unless Option 2 appropriately demonstrates these changes.
3. **Option C: Option 2 is the graph of \( f(x - 7) \)**
This would shift the graph of \( f(x) \) horizontally to the right by 7 units. Given the original function shifts the sine graph vertically up by 2, this option changes its horizontal position. If Option 2 does not demonstrate this horizontal shift, it isn't valid.
4. **Option D: Option 2 is the graph of \( f(-x) \)**
This transformation reflects the graph across the y-axis. For this option to be correct, we would see a mirror image of the graph of \( f(x) = \sin(x) + 2 \) on the left side of the y-axis.
Without the visual representation of Option 2, it's difficult to definitively choose the correct answer. However, consider the characteristics of the transformations involved:
- If Option 2 represents a vertical shift upwards or downwards without flipping or reflecting, then none of these options would apply.
- If it appears to be a horizontal shift to the right, option C would be correct, if it matches that description.
- If there are reflections involved, options A, B, or D may be designated based on the direction of the reflection.
In conclusion, please check the visual representation of Option 2 against the transformations described to choose the correct option.