SOLUTION: Given f(x) = 3x + 1, and g(x) = -2 • f(x) - 1. Describe the transformations(list them) and write the new simplified equation for g(x).
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Question 1199724: Given f(x) = 3x + 1, and g(x) = -2 • f(x) - 1. Describe the transformations(list them) and write the new simplified equation for g(x).
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**1. Transformations:**
* **Vertical Stretch:** The coefficient -2 stretches the graph of f(x) vertically by a factor of 2.
* **Reflection in the x-axis:** The negative sign in front of -2f(x) reflects the graph of f(x) across the x-axis.
* **Vertical Shift:** The "-1" at the end of the equation shifts the graph of -2f(x) downward by 1 unit.
**2. Simplified Equation for g(x)**
* g(x) = -2 * f(x) - 1
* g(x) = -2 * (3x + 1) - 1
* g(x) = -6x - 2 - 1
* g(x) = -6x - 3
**Therefore:**
* The transformations applied to f(x) to obtain g(x) are: vertical stretch by a factor of 2, reflection in the x-axis, and a vertical shift downward by 1 unit.
* The simplified equation for g(x) is g(x) = -6x - 3.
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