Question

If g(x) = -f(x+2), what type of transformation is applied to the function f(x)?

a) Reflection over the x-axis and a horizontal shift to the left by 2 units
b) Reflection over the y-axis and a horizontal shift to the right by 2 units
c) Vertical stretch by a factor of 2 and a horizontal shift to the right by 2 units
d) Vertical compression by a factor of 2 and a horizontal shift to the left by 2 units

Answer 1

The type of transformation applied to the function f(x) in the equation g(x) = -f(x+2) is a reflection over the y-axis and a horizontal shift to the left by 2 units.

Step-by-step explanation:

The type of transformation applied to the function f(x) in the equation g(x) = -f(x+2) is a reflection over the y-axis and a horizontal shift to the left by 2 units.

When g(x) = -f(x+2), the negative sign in front of f(x+2) indicates a reflection over the y-axis, meaning the graph of f(x) will be mirrored across the y-axis. The addition of 2 inside the function notation x+2 indicates a horizontal shift to the left by 2 units.