Hope this is straightforward.
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Answer:
(d) The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Step-by-step explanation:
We assume you intend ...
f(x) = equation of a parabola
g(x) = 2/3·f(x)
Multiplying a function by a factor of 2/3 will cause it to be compressed vertically to 2/3 of its original height. When the function is a parabola, this has the effect of making it appear wider than before the compression.
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The compression factor is positive, so points on the graph remain on the same side of the x-axis. The direction in which the graph opens is not changed.
The attachment shows parabolas that open upward and downward, along with the transformed version.
