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what kind of transformation converts the graph of f(x) = -6x + 2 into the graph of g(x) = 6x + 2?
what kind of transformation converts the graph of f(x) = -6x + 2 into the graph of g(x) = 6x + 2?
Answers
GPT-4o mini
To determine the transformation that converts the graph of \( f(x) = -6x + 2 \) into the graph of \( g(x) = 6x + 2 \), we can analyze the changes in the function's form.
1. **Identify the slopes:**
- The slope of \( f(x) \) is -6.
- The slope of \( g(x) \) is 6.
2. **Understanding the transformation:**
- The change from a slope of -6 to 6 indicates a reflection across the x-axis (which inverts the sign of the slope) followed by a transformation that doesn't affect the vertical shift, which is represented by the constant term (which remains 2 in both functions).
3. **Describe the transformation:**
- Therefore, the transformation can be described as:
- **Reflection across the x-axis**: This changes \( f(x) \) from \( -6x + 2 \) to \( 6x + 2 \).
Thus, the transformation that converts \( f(x) = -6x + 2 \) into \( g(x) = 6x + 2 \) is a reflection across the x-axis.
1. **Identify the slopes:**
- The slope of \( f(x) \) is -6.
- The slope of \( g(x) \) is 6.
2. **Understanding the transformation:**
- The change from a slope of -6 to 6 indicates a reflection across the x-axis (which inverts the sign of the slope) followed by a transformation that doesn't affect the vertical shift, which is represented by the constant term (which remains 2 in both functions).
3. **Describe the transformation:**
- Therefore, the transformation can be described as:
- **Reflection across the x-axis**: This changes \( f(x) \) from \( -6x + 2 \) to \( 6x + 2 \).
Thus, the transformation that converts \( f(x) = -6x + 2 \) into \( g(x) = 6x + 2 \) is a reflection across the x-axis.