If g(x) = -f(x), describe the transformation that results in g(x(

Question

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.