The g(x) = f(-x) + 3 is the transformation of f(x). Which of the following is the correct description of transformation?

(1 Point)

g(x) reflects f(x) across x - axis and translated 3 units upward.

g(x) reflects f(x) across y - axis and translated 3 units upward.

g(x) reflects f(x) across y - axis and translated 3 units to the left.

g(x) reflects f(x) across x - axis and translated 3 units upward.

The correct transformation of \( g(x) = f(-x) + 3 \) can be described as follows:

1. **Reflection across the y-axis**: The negative sign inside the function, \( f(-x) \), reflects the function \( f(x) \) across the y-axis.
2. **Vertical translation**: The \( +3 \) outside the function adds 3 units, which shifts the graph of \( f(-x) \) vertically upward by 3 units.

Thus, the correct description is:

**g(x) reflects f(x) across the y-axis and is translated 3 units upward.**

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Do you want more details or have any questions? Here are some related questions to explore:

1. How do different transformations (e.g., \(f(x) + c\), \(f(x - c)\)) affect the graph of a function?
2. What is the effect of reflecting a function across the x-axis versus the y-axis?
3. How can you identify a vertical or horizontal stretch/compression in a function transformation?
4. What happens when multiple transformations (e.g., reflection and translation) are applied to a function?
5. Can you describe the impact of a horizontal shift to the left or right on a function's graph?

**Tip:** When analyzing transformations, always pay attention to whether changes occur inside or outside the function to determine horizontal or vertical effects.

The g(x) = f(-x) + 3 is the transformation of f(x). Which of the following is the correct description of transformation? (1 Point) g(x) reflects f(x) across x - axis and translated 3 units upward. g(x) reflects f(x) across y - axis and translated 3 units upward. g(x) reflects f(x) across y - axis and translated 3 units to the left. g(x) reflects f(x) across x - axis and translated 3 units upward.

Explore how the function g(x) = f(-x) + 3 reflects across the y-axis and is translated 3 units upward. This problem highlights key concepts in function transformations, including reflection and vertical translation. Ideal for students in Grades 9-12.

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