Answer:
A. The graph of g(x) is horizontally compressed by a factor of 3
Explanation:
You want to compare f(x) = x² with g(x) = (3x)².
Horizontal compression
Replacing x with cx in a function definition causes its graph to be horizontally compressed by a factor of c.
In the given case, c=3, so the compression is by a factor of 3.
If you consider a value of x, this can become clear. For x=6 in the original function, we have ...
f(6) = 6² = 36
We get the same function value for x=2 in the compressed function:
g(2) = (3·2)² = 36
That is, the point (6, 36) on the graph of f(x) is moved to (2, 36) on the graph of g(x). It is 1/3 the distance from the y-axis, indicating compression horizontally by a factor of 3.
The graph of g(x) is compressed horizontally by a factor of 3, choice A.
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Additional comment
The function g(x) can be expanded to the form ...
g(x) = 9x²
In this form it indicates g(x) is a vertical stretch of f(x) by a factor of 9. The point (2, 4) on the graph of f(x) becomes the point (2, 36) on the graph of g(x).
Depending on the function, a vertical stretch by some amount may be equivalent to a horizontal compression (or stretch) by some other amount.
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