Question

Which of the following best describes the transformation g(x) = f(x + 3)?

A) A horizontal shift of f(x) to the right by 3 units.

B) A vertical shift of f(x) upwards by 3 units.

C) A reflection of f(x) over the x-axis followed by a horizontal shift of 3 units to the right.

D) A reflection of f(x) over the y-axis followed by a horizontal shift of 3 units to the left.

Answer 1

The transformation g(x) = f(x + 3) causes a horizontal shift of the function f(x) to the right by 3 units, making option A the correct answer.

Step-by-step explanation:

The transformation g(x) = f(x + 3) represents a horizontal shift of the original function f(x) to the right by 3 units. When you add a positive constant inside the function's argument, you shift the graph horizontally in the opposite direction of the sign; in this case, since we add 3, we move horizontally to the right side of the coordinate system. Therefore, the correct answer is A) A horizontal shift of f(x) to the right by 3 units. This is because the transformation does not affect the y-values, but instead, it moves every point on the graph of f(x) to the right by 3 units along the x-axis. This type of transformation neither reflects the function over an axis nor affects its vertical position.