How is the graph of g (x) = f (kx) related to the graph of f when k = 5?

A. The graph of g is a horizontal stretch of the graph of f.

B. The graph of g is a vertical stretch of the graph of f.

C. The graph of g is a horizontal compression of the graph of f.

D. The graph of g is a vertical compression of the graph of f.

Question

Mathematics

Magdalena Mathis

21 November, 14:15

How is the graph of g (x) = f (kx) related to the graph of f when k = 5?

A. The graph of g is a horizontal stretch of the graph of f.

B. The graph of g is a vertical stretch of the graph of f.

C. The graph of g is a horizontal compression of the graph of f.

D. The graph of g is a vertical compression of the graph of f.

+2

Answers (1)

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Becker · Answer 1

The graph of g is a horizontal compression of the graph of f.

Step-by-step explanation:

When we multiply a constant positive number to the domain of the function, the variations on the "x" axis have a greater impact on the "y" axis. In this case for the original function every variation on the "x" axis would imply on a variation of the "y" axis, but on the new function where we have "f (kx) " with "k = 5", every variation on the "x" axis implies on 5 times the original value of the variation on the "y" axis, so for a smaller interval in the "x" axis we have more information about the "y" axis than before. Therefore, the graph gets compressed horizontally.