To analyze the transformation from the function \( f(x) = \frac{1}{x} \) to the function \( k(x) = -\frac{3}{4}x \), we need to break down the changes step by step.
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Reflection: The negative sign in front of the \( \frac{3}{4}x \) indicates a reflection across the x-axis.
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Vertical Stretch/Compression: The factor \( \frac{3}{4} \) indicates a vertical compression by a factor of \( \frac{3}{4} \). This is because a factor less than 1 compresses the function vertically.
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Horizontal Stretch/Compression/Transformation: The expression \( x \) in \( -\frac{3}{4}x \) is not altered (there is no division or multiplication by \( x \)), so there is no horizontal stretch or compression from the basic function \( f(x) = \frac{1}{x} \).
Given these transformations, we conclude that:
- The function is reflected across the x-axis because of the negative sign.
- The function is vertically compressed by a factor of \( \frac{3}{4} \).
Thus, the correct choice is:
It vertically compresses by a factor of \( \frac{3}{4} \) and reflects across the x-axis.