Which transformation reflects a graph across the x-axis?

Which transformation reflects a graph across the x-axis?

• A. g(x) = f(x)
• B. g(x) = -f(x)
• C. g(x) = f(-x)
• D. g(x) = -f(-x)

Answer: (B)

Reflecting a graph across the x-axis means turning every y-value into its opposite while the x-coordinate stays the same. In function form, that transformation is g(x) = -f(x), because each point (x, f(x)) becomes (x, -f(x)). Graphically, you flip the original curve over the horizontal axis, so peaks become valleys and vice versa, with x-values unchanged. The other forms do different reflections: g(x) = f(-x) mirrors across the y-axis, and g(x) = -f(-x) flips across both axes (a 180-degree rotation about the origin). Therefore, the reflection across the x-axis corresponds to g(x) = -f(x).

Reflecting a graph across the x-axis means turning every y-value into its opposite while the x-coordinate stays the same. In function form, that transformation is g(x) = -f(x), because each point (x, f(x)) becomes (x, -f(x)). Graphically, you flip the original curve over the horizontal axis, so peaks become valleys and vice versa, with x-values unchanged. The other forms do different reflections: g(x) = f(-x) mirrors across the y-axis, and g(x) = -f(-x) flips across both axes (a 180-degree rotation about the origin). Therefore, the reflection across the x-axis corresponds to g(x) = -f(x).