Question

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



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

Answer 1

To analyze the transformation of the function \( f(x) \) into \( -3 \times f(x) \):

1. The coefficient \(-3\) indicates two transformations:
- The negative sign \(-\) reflects the graph about the x-axis.
- The \(3\) (which is greater than 1) indicates a vertical stretch of the graph by a factor of 3.

Thus, the overall transformation will be characterized as the graph being reflected about the x-axis and stretched vertically.

So, the correct description of the graph of \( -3 \times f(x) \) is:

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