The coordinate plane shows the graph of the quadratic function f(x) .

Question

A parabola open up and passes through (6, 14), (5, 6), (4, 0), (1, -9), (0, -8), (-2, 0), (-3, 7), and (4, 15).

Which of the following describes the graph of -3 x f(x) ?

A. The graph of f(x) is widened horizontally and reflected about the y-axis.

B. The graph of f(x) is widened horizontally and reflected about the x-axis.

C. The graph of f(x) is stretched vertically and reflected about the x-axis.

D. The graph of f(x) is stretched vertically and reflected about the y-axis.

Answer 1

To analyze the transformation represented by the function \(-3f(x)\) compared to the original function \(f(x)\), we can break down the components of this transformation:

1. Reflection: The negative sign in front of \(3\) indicates that the graph of \(f(x)\) is reflected about the x-axis. This means that all the y-values of the function will change sign.

2. Vertical Stretch: The coefficient \(3\) indicates a vertical stretch. The graph of \(f(x)\) will be stretched away from the x-axis by a factor of 3. This means that the y-values will be multiplied by 3.

Putting these two transformations together, we see that \(-3f(x)\) will impose both a reflection about the x-axis and a vertical stretch by a factor of 3.

Given this analysis, the correct choice from the options provided is:

C. The graph of f(x) is stretched vertically and reflected about the x-axis.