Which of the following correctly analyzes the effects on the reciprocal parent function when

f(x) = 1/x is replaced by f (x) = 1/-3.14x? (1 point)
The reciprocal parent function undergoes a horizontal compression and a reflection across the y-
axis.
The reciprocal parent function undergoes a horizontal stretch and a reflection across the y-axis.
The reciprocal parent function undergoes a horizontal compression.
◇ The reciprocal parent function undergoes a horizontal stretch.

1 answer

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.

  1. 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).

  2. 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.