Final Answer:
The negative sign in front of f(x) in the function g(x) = -f(x) signifies a reflection across the x-axis. Therefore, the effect on the parent function is a vertical reflection. Thus the correct option is A
Step-by-step explanation:
The parent function is f(x) = 3x - 1.
The parent function f(x) = 3x - 1 is a linear function with a slope of 3 and a y-intercept of -1. It represents a straight line sloping upwards.
Understanding the transformation in g(x) = -f(x) = 3x - 1:
The negative sign in front of f(x) indicates a vertical reflection across the x-axis.
Analyzing the effect:
The negative sign in g(x) = -f(x) reflects the parent function f(x) = 3x - 1 across the x-axis, causing all the y-values to become their opposites (positive values become negative, and negative values become positive). This reflects the graph of the function vertically.
There's no horizontal compression or stretching involved because the coefficient before x remains the same in both functions f(x) and g(x).
Therefore, the effect of the function g(x) = -f(x) = 3x - 1 on the parent function f(x) = 3x - 1 is a vertical reflection across the x-axis.
Therefore, the correct option is A.