Question

Write the function rule​ g(x) after the given transformations of the graph of ​f(x)equalsnegative 4x.
reflection in the x​-axis; vertical compression by a factor of one eighth
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Part 1
​g(x)equals
  
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Answer 1

To find the function rule \( g(x) \) after applying the transformations to the function \( f(x) = -4x \), we need to follow the specified transformations step by step.

1. **Reflection in the x-axis:** This changes the sign of the function. If \( f(x) = -4x \), after reflecting it in the x-axis, we have:
\[
-f(x) = -(-4x) = 4x
\]

2. **Vertical compression by a factor of one eighth:** For a vertical compression by a factor of \( \frac{1}{8} \), we multiply the function by \( \frac{1}{8} \). Thus:
\[
g(x) = \frac{1}{8} \cdot (4x) = \frac{4}{8} x = \frac{1}{2} x
\]

Now we combine the transformations to arrive at the final function rule for \( g(x) \):
\[
g(x) = \frac{1}{2} x
\]

So the final answer is:
\[
g(x) = \frac{1}{2} x
\]