Select the correct answer.

Question

Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = -8f(x)?
A.
It is the graph of f(x) reflected about the x-axis and shrunk vertically by a factor of 8.
B.
It is the graph of f(x) reflected about the x-axis and stretched vertically by a factor of 8.
C.
It is the graph of f(x) reflected about the y-axis and shrunk vertically by a factor of 8.
D.
It is the graph of f(x) reflected about the y-axis and stretched horizontally by a factor of 8.

Answer 1

To analyze the transformation described by \( g(x) = -8f(x) \), where \( f(x) = x \), let's break down the components:

• The negative sign (−) indicates that the graph is reflected about the x-axis.
• The factor of 8 indicates a vertical transformation. Since it is a multiplication by 8, it means the graph is vertically stretched by a factor of 8.

Putting these transformations together, we conclude that \( g(x) \) is the graph of \( f(x) \) reflected about the x-axis and stretched vertically by a factor of 8.

Thus, the correct answer is:

B. It is the graph of f(x) reflected about the x-axis and stretched vertically by a factor of 8.