If the function f(x)=(x−3)2−5

Question

is reflected horizontally across the y-axis, how does the reflection affect the point (2,−4)
?(1 point)
Responses

In the horizonal reflection, the point (2,−4)
becomes (−4,2)
In the horizonal reflection, the point open paren 2 comma negative 4 close paren becomes open paren negative 4 comma 2 close paren

In the horizonal reflection, the point (2,−4)
becomes (−2,4)
In the horizonal reflection, the point open paren 2 comma negative 4 close paren becomes open paren negative 2 comma 4 close paren

In the horizonal reflection, the point (2,−4)
becomes (−2,−4)
In the horizonal reflection, the point open paren 2 comma negative 4 close paren becomes open paren negative 2 comma negative 4 close paren

In the horizonal reflection, the point (2,−4)
becomes (2,4)

Answer 1

When a point is reflected horizontally across the y-axis, the x-coordinate of the point changes sign, while the y-coordinate remains the same.

For the point \((2, -4)\):

• The x-coordinate is \(2\); reflecting it across the y-axis changes it to \(-2\).
• The y-coordinate \(-4\) remains unchanged.

Therefore, the reflected point becomes \((-2, -4)\).

So the correct response is:

In the horizonal reflection, the point (2,−4) becomes (−2,−4). In the horizonal reflection, the point open paren 2 comma negative 4 close paren becomes open paren negative 2 comma negative 4 close paren.