$$ f(x)=9 x ; g(x)=\frac{9 x}{10}-7 $$ 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

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UpStudy AI · Accepted Answer

Let’s start with the given functions:
$$
f(x)=9x \quad \text{and} \quad g(x)=\frac{9x}{10}-7.
$$
We can rewrite $$ g(x) $$ in terms of $$ f(x) $$. Notice that
$$
g(x)=\frac{9x}{10}-7 = \frac{1}{10}\,(9x)-7 = \frac{1}{10}\,f(x)-7.
$$

This shows that the graph of $$ f(x)=9x $$ is transformed in two steps to obtain the graph of $$ g(x) $$:

1. **Vertical Compression:** Multiply $$ f(x) $$ by $$\frac{1}{10}$$. This compresses the graph vertically by a factor of $$\frac{1}{10}$$.

2. **Vertical Translation:** Subtract 7 from the result, which shifts the graph downward by 7 units.

Since the multiplication (compression) is applied first and then the subtraction (translation), the correct description is:

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

Among the given options, the one that correctly identifies the first transformation is the one stating “First there is a vertical compression by a factor …”. Hence, the correct answer is:

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

\( f(x)=9 x ; g(x)=\frac{9 x}{10}-7 \) 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

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