If the function f(x)=(x+1)2

Question

is reflected horizontally, how does the reflection affect the point (−2,1)
?(1 point)
Responses

In the horizontal reflection, the point (−2,1)
becomes (−2,−1)
.
In the horizontal reflection, the point left parenthesis negative 2 comma 1 right parenthesis becomes left parenthesis negative 2 comma negative 1 right parenthesis .

In the horizontal reflection, the point (−2,1)
becomes (2,−1)
.
In the horizontal reflection, the point left parenthesis negative 2 comma 1 right parenthesis becomes left parenthesis 2 comma negative 1 right parenthesis .

In the horizontal reflection, the point (−2,1)
becomes (1,2)
.
In the horizontal reflection, the point left parenthesis negative 2 comma 1 right parenthesis becomes left parenthesis 1 comma 2 right parenthesis .

In the horizontal reflection, the point (−2,1)
becomes (2,1)
.

Answer 1

To understand how a horizontal reflection affects the point \((-2, 1)\), we need to clarify what a horizontal reflection entails.

A horizontal reflection across the y-axis changes the x-coordinate of a point to its negative. This means:

\[ (x, y) \rightarrow (-x, y) \]

For the point \((-2, 1)\):

1. The x-coordinate \(-2\) becomes \(-(-2) = 2\).
2. The y-coordinate remains the same, which is \(1\).

Therefore, the point \((-2, 1)\) after a horizontal reflection becomes:

\[ (2, 1) \]

Thus, the correct response is:

In the horizontal reflection, the point \((-2, 1)\) becomes \((2, 1)\).