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−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 negative f times negative x.
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)
.
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−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 negative f times negative x.
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)
.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.
1. **\( f(x) = \sin x + 2 \)**: This is the basic sine wave shifted vertically upwards by 2 units.
2. 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. **\( f(x) = \sin x + 2 \)**: This is the basic sine wave shifted vertically upwards by 2 units.
2. 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)**.
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