Question

Which statement correctly describes the relationship between the graph of f(x) = x and the graph of g(x) = f (x) - 2 ?

A. The graph of g(x) is the graph of f(x) translated 2 units down.
B. The graph of g(x) is the graph of f (c) vertically compressed by a factor of 2.
C. The graph of g() is the graph of f (2) vertically stretched by a factor of 2.
D. The graph of g (c) is the graph of f (x) translated 2 units left.

Answer 1

Statement A is correct; the graph of g(x) is the original graph f(x) translated 2 units down vertically.

Step-by-step explanation:

The question is related to understanding how the graph of one function, g(x) = f(x) - 2, is related to another, f(x) = x. Given that f(x) is a standard linear function, when we subtract 2 from this function to get g(x), we are effectively translating the graph vertically downward by 2 units. This is because the vertical translation of a graph involves shifting the graph up or down in the coordinate plane without altering its shape. Therefore, statement A is correct: The graph of g(x) is the graph of f(x) translated 2 units down.