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

Question

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

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

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

Answer 1

In mathematics, a horizontal reflection across the x-axis transforms a point \((x, y)\) to \((x, -y)\).

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

• The x-coordinate remains the same: \(-2\)
• The y-coordinate is negated, changing from \(1\) to \(-1\)

Thus, the reflection of the point \((-2, 1)\) will be:

\[ (-2, 1) \rightarrow (-2, -1) \]

Therefore, the correct response is:

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