Question

Which of the following best describes a function transformation in the formulation g(x) = f(x) + a?

A) A horizontal translation of the graph of f(x).
B) A vertical translation of the graph of f(x).
C) A reflection of the graph of ƒ (x across the x-axis.
D) A horizontal compression or stretching of the graph of f(x).

Answer 1

The function transformation described in g(x) = f(x) + a is a vertical translation of the graph of f(x).

Step-by-step explanation:

The function transformation described in the formulation g(x) = f(x) + a is a vertical translation of the graph of f(x). Adding a constant value 'a' to the function f(x) shifts the entire graph vertically either upward or downward.

For example, if f(x) represents a straight line with a slope of 1, and a value of 2 is added to the function, the graph of g(x) will be the same line shifted 2 units upward.

Therefore, option B) A vertical translation of the graph of f(x) best describes the function transformation in the formulation g(x) = f(x) + a.