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Which transition shifts the graph of f(x) = 3x + 3 onto g(x) = 3x - 3?

a) Vertical shift up by 3 units
b) Vertical shift down by 3 units
c) Horizontal shift to the right by 3 units
d) Horizontal shift to the left by 3 units

1 Answer

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Final answer:

The graph of f(x) = 3x + 3 is shifted onto g(x) = 3x - 3 by a vertical shift down by 3 units, directly changing the y-intercept to match g(x).

Step-by-step explanation:

The student is asked to identify the transformation that shifts the graph of f(x) = 3x + 3 to g(x) = 3x - 3. The only difference between these two equations is the y-intercept; for f(x), the y-intercept is +3, and for g(x), the y-intercept is -3. This change does not affect the slope of the line, which remains at 3 in both equations. Therefore, the transformation from f(x) to g(x) would involve a vertical shift down by 6 units, as we need to subtract 6 from the y-intercept of f(x) to match the y-intercept of g(x).

The correct answer is b) Vertical shift down by 3 units, as this directly changes the y-intercept from +3 to -3. A vertical shift up would increase the y-intercept, while a horizontal shift to the left or right would change the x-intercepts and is not related to this specific transformation.

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