Question
The coordinate plane shows the graph of the quadratic function f(x)f(x). Which of the following describes the graph −3×f(x)−3×f(x)? (1 point) Responses 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 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 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 stretched vertically and reflected about the y-axis The graph of f(x) is stretched vertically and reflected about the y-axis
Answers
GPT-4o mini
To analyze the transformation of the function \( -3f(x) \), we need to break it down into two parts:
1. The negative sign (-) indicates a reflection about the x-axis.
2. The factor of 3 indicates a vertical stretch by a factor of 3.
Putting these effects together, the graph of \( -3f(x) \) can be described as follows:
- The graph of \( f(x) \) is reflected about the x-axis (due to the negative sign).
- The graph is also stretched vertically by a factor of 3 (due to the multiplication by 3).
Therefore, the correct description of the graph of \( -3f(x) \) is:
**The graph of f(x) is stretched vertically and reflected about the x-axis.**
1. The negative sign (-) indicates a reflection about the x-axis.
2. The factor of 3 indicates a vertical stretch by a factor of 3.
Putting these effects together, the graph of \( -3f(x) \) can be described as follows:
- The graph of \( f(x) \) is reflected about the x-axis (due to the negative sign).
- The graph is also stretched vertically by a factor of 3 (due to the multiplication by 3).
Therefore, the correct description of the graph of \( -3f(x) \) is:
**The graph of f(x) is stretched vertically and reflected about the x-axis.**