Question

What is the effect on the graph of f(x)=x−−√3
when f(x)
is replaced by −2f(x)
?(1 point)
Responses

The graph is reflected across the x-axis and has been stretched vertically.
The graph is reflected across the x -axis and has been stretched vertically.

The graph is reflected across the x-axis and has been stretched horizontally.
The graph is reflected across the x -axis and has been stretched horizontally.

The graph is reflected across the y-axis and has been compressed vertically.
The graph is reflected across the y -axis and has been compressed vertically.

The graph is reflected across the y-axis and has been compressed horizontally.

Answer 1

The transformation of \( f(x) = \sqrt{x} \) to \( -2f(x) \) implies the following changes:

1. **Reflection across the x-axis**: The negative sign in front of \( f(x) \) indicates that the graph is flipped over the x-axis.

2. **Vertical Stretch**: The factor of 2 means that the graph is stretched vertically by a factor of 2.

Thus, when \( f(x) \) is replaced by \( -2f(x) \), we see that the correct choice is:

**The graph is reflected across the x-axis and has been stretched vertically.**