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 stretches vertically by a scale factor of 2.
The graph stretches vertically by a scale factor of 2.

The graph stretches horizontally by a scale factor of 2.
The graph stretches horizontally by a scale factor of 2.

The graph shifts down 2 units.
The graph shifts down 2 units.

The graph shifts right 2 units.
The graph shifts right 2 units.

Answer 1

When the function \( f(x) = \sqrt{x} - 3 \) is replaced by \( 2f(x) \), the new function becomes \( 2f(x) = 2(\sqrt{x} - 3) = 2\sqrt{x} - 6 \).

This transformation involves multiplying the entire function by 2, which affects the vertical scaling of the graph.

**Therefore, the correct response is:**

**The graph stretches vertically by a scale factor of 2.**