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

Question

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

(1 point)
Responses

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

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

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

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

Answer 1

To analyze the transformation of the quadratic function \( f(x) \) when we change it to \( -3 \times f(x) \), we need to consider the two components of the transformation:

1. The multiplication by -1: This reflects the graph about the x-axis. So, any point \( (x, f(x)) \) on the graph of \( f(x) \) will be transformed to \( (x, -f(x)) \).

2. The multiplication by 3: This vertically stretches the graph by a factor of 3. In this case, the point \( (x, f(x)) \) will be transformed to \( (x, -3f(x)) \), which means the y-values are multiplied by 3 (after the reflection).

Given these transformations, we can conclude that the graph of \( -3 \times f(x) \) is stretched vertically by a factor of 3 and reflected about the x-axis.

Thus, the correct response is:

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