Question

""The graph of the parent function f(x) = x^3 is transformed such that g(x) = (-1/2x^3). Which statements about the graph of g(x) are accurate?

A) The graph of g(x) is a horizontal reflection of the graph of f(x).
B) The graph of g(x) is a vertical reflection of the graph of f(x).
C) The graph of g(x) is a vertical compression of the graph of f(x).
D) The graph of g(x) is a vertical stretch of the graph of f(x).

Please select the statements that accurately describe the transformation of the graph from f(x) to g(x).""

Answer 1

The graph of g(x) = (-1/2x^3) is both a vertical reflection and a vertical compression of the parent function f(x) = x^3. The negative sign in -1/2 indicates the reflection, and the 1/2 indicates the compression.

Step-by-step explanation:

The transformation of the parent function f(x) = x^3 to g(x) = (-1/2x^3) involves a couple of specific changes to the graph. The coefficient -1/2 before the x^3 term indicates two transformations.

• The negative sign indicates a reflection over the x-axis, meaning that each point on the graph of f(x) is flipped vertically to the opposite side of the x-axis.
• The fraction 1/2 indicates a vertical compression by a factor of 1/2. This means that the y-values of the original function are halved, making the graph of g(x) appear 'squished' compared to the graph of f(x).

Therefore, the correct statements that describe the transformation from f(x) to g(x) are:

• B) The graph of g(x) is a vertical reflection of the graph of f(x).
• C) The graph of g(x) is a vertical compression of the graph of f(x).