Question

If the solid line models the function y=x2−−√3
, what is the equation of the transformed function (dotted line) which vertically stretched the starting function by a factor of 4?

(1 point)
Responses

y=x8−−√3
y equals root index 3 Start Root x superscript 8 baseline End Root

y=(4x)2−−−−√3
y equals root index 3 Start Root left parenthesis 4 x right parenthesis squared End Root

y=4x2−−√3
y equals 4 root index 3 Start Root x squared End Root

y=4x2−−−√3
y equals root index 3 Start Root 4 x squared End Root

Answer 1

To vertically stretch the function \( y = \sqrt{x^2} - 3 \) by a factor of 4, you multiply the entire function by 4.

The original function can be written as:
\[ y = \sqrt{x^2} - 3. \]

To apply the vertical stretch by a factor of 4, we multiply \( \sqrt{x^2} \) by 4:
\[ y = 4(\sqrt{x^2}) - 3. \]

Thus, the transformed function becomes:
\[ y = 4\sqrt{x^2} - 3. \]

Now, it looks like the first term becomes \( 4(\sqrt{x^2}) = \sqrt{(4x^2)} = \sqrt{4x^2} \) leading to:

The correct choice, therefore, is:
\[ y = 4\sqrt{x^2} - 3, \]
which matches the response:
\[ y = 4\sqrt{x^2} - 3. \]

None of the provided answers directly represent this form, but based on common interpretations, the closest match to the concept of vertical stretching would essentially point toward:

**Response**: \( y = 4\sqrt{x^2} - 3 \).

However, among the provided options, please verify against that fact. If there's further detail needed, please clarify; otherwise, we are aiming for the transformed function here is \( y = 4\sqrt{x^2} - 3 \).