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  (a)  vertical compression by a factor of 1/3

Step-by-step explanation:

We can see that g(x) = 1/3f(x). Multiplying a function by a constant scales the graph vertically by that factor. When the magnitude of the factor is more than 1, we say the graph is "stretched." When it is less than 1, we say the graph is "compressed" by that factor.

Here, the scale factor is 1/3, so the graph is "vertically compressed by a factor of 1/3."

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Additional comment

My personal preference is for compression to be described by the factor the graph is divided by. I would call g(x) a compression of f(x) by a factor of 3. Modern curriculum authors disagree, calling it compression by a factor of 1/3.

Be careful. Using the currently accepted language, a stretch is always by a number larger than 1, and a compression is always by a number less than 1. This rules out choices C and D simply on the basis of the language used.

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For many graphs, vertical scaling and horizontal scaling can be interchanged. We note that g(x) is wider than f(x), so could be stretched horizontally by some factor. That factor would be √3. The equation using a horizontal stretch factor would be g(x) = (x/√3)^2. Replacing x by x/k is a stretch by a factor of k in the horizontal direction.

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step-by-step explanation:

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step-by-step explanation: