Question

The graph of g(x) = 4x is a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x)? A. The graph of g(x) is one-fourth of a unit to the left of the graph of f(x). B. The graph of g(x) is four units to the left of the graph of f(x). C. The graph of g(x) is one-fourth as steep as the graph of f(x). D. The graph of g(x) is four times as steep as the graph of f(x).

Answer 1

The graph of g(x) = 4x is a vertical stretch of the graph of f(x) = x, making g(x) four times as steep as f(x). The correct answer is D.

Step-by-step explanation:

The correct statement that describes the graph of g(x) = 4x as a transformation of the graph of f(x) = x is The graph of g(x) is four times as steep as the graph of f(x).

To understand this transformation, let's compare the slopes of the two functions. The slope of f(x) is 1, which means for every 1 unit increase in x, there is a corresponding 1 unit increase in y.

The slope of g(x) is 4, which means for every 1 unit increase in x, there is a corresponding 4 unit increase in y. Therefore, g(x) is four times as steep as f(x).