Question

If g(x) = -f(x), describe the transformation that results in g(x(
Reflection over y-axis
Over x-axis
Translating 1unit to right
1 unit to left

Answer 1

The function \( g(x) = -f(x) \) represents a transformation of the function \( f(x) \). This specific transformation indicates a reflection over the x-axis.

Here's a brief explanation of the transformations mentioned:

- **Reflection over y-axis**: This would be represented by a function like \( f(-x) \), which reflects the graph across the y-axis.
- **Reflection over x-axis**: This is what \( g(x) = -f(x) \) represents; the graph of \( f(x) \) is flipped over the x-axis.
- **Translating 1 unit to the right**: This transformation would be represented by \( f(x - 1) \).
- **Translating 1 unit to the left**: This would be represented as \( f(x + 1) \).

So, the correct answer is that the transformation resulting in \( g(x) = -f(x) \) is a reflection over the x-axis.