Question

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What is the effect on the graph of the function f(x) = x when f(x) is replaced with −1/2f(x)?
A) vertical reflection over x-axis and vertical stretch
B) vertical reflection over x-axis and vertical compression
C) horizontal reflection over y-axis and horizontal stretch
D) horizontal reflection over y-axis and horizontal compression

Answer 1

When the function f(x) is replaced with -1/2f(x), it results in vertical reflection over x-axis and vertical compression of the graph.

Step-by-step explanation:

When the function f(x) is replaced with -1/2f(x), it means that the values of the original function are multiplied by -1/2. This has two effects on the graph of the function:

1. Vertical reflection over the x-axis: The positive values of f(x) become negative and vice versa. This flips the graph of the function vertically.
2. Vertical stretch: The values of f(x) are multiplied by -1/2, which compresses the graph vertically. The new graph will be half as tall as the original graph.

Therefore, the correct answer is B) vertical reflection over x-axis and vertical compression.