To analyze the transformation of the reciprocal parent function \( f(x) = \frac{1}{x} \) to \( f(x) = \frac{1}{-3.14x} \), we can break down the changes step-by-step.
-
Reflection: The negative sign in front of the \( 3.14x \) indicates that there will be a reflection across the y-axis (since replacing \( x \) with \( -x \) reflects the function across the y-axis).
-
Horizontal Compression: The coefficient \( 3.14 \) in the term \( -3.14x \) affects the horizontal scaling. When there is a constant multiplied by \( x \) in the denominator of a rational function, it results in a horizontal compression. Specifically, a factor greater than 1 (like \( 3.14 \)) compresses the function horizontally.
Putting this together, we find that the correct analysis of the transformation from \( f(x) = \frac{1}{x} \) to \( f(x) = \frac{1}{-3.14x} \) includes both a horizontal compression and a reflection across the y-axis.
Thus, the correct answer is:
The reciprocal parent function undergoes a horizontal compression and a reflection across the y-axis.