Question
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\( f(x)=9 x ; g(x)=\frac{9 x}{10}-7 \) Choose the correct answer below. A. First there is a vertical translation down \( \frac{1}{10} \) ur B. First there is a vertical compression by a fact C. First there is a vertical translation down 7 units D. First there is a vertical compression by a facte

Ask by Fowler Vega. in the United States
Mar 11,2025

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Answer

First, there is a vertical compression by a factor of \(\frac{1}{10}\), then a vertical translation down 7 units.

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Extra Insights

To understand the relationship between the functions \( f(x) \) and \( g(x) \), notice that \( g(x) \) modifies \( f(x) \) by applying a vertical translation and a vertical compression. The original function \( f(x) = 9x \) is adjusted by scaling down its output by a factor of \( \frac{9}{10} \) and then translating it downward by 7 units. Thus, the correct choice among the options provided is C: First there is a vertical translation down 7 units. This option captures the transformation after the initial vertical compression, which is implied when viewing how \( g(x) \) is derived from \( f(x) \).

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