Question

The function f(x)=(x+1)2
𝑓
(
𝑥
)
=
(
𝑥
+
1
)
2
is reflected over the x-axis to create g(x)
𝑔
(
𝑥
)
. Identify the equation for g(x)
𝑔
(
𝑥
)
.(1 point)
Responses

g(x)=−(x+1)2
𝑔
(
𝑥
)
=
−
(
𝑥
+
1
)
2

g left parenthesis x right parenthesis equals negative left parenthesis x plus 1 right parenthesis squared

g(x)=(−x−1)2
𝑔
(
𝑥
)
=
(
−
𝑥
−
1
)
2

g left parenthesis x right parenthesis equals left parenthesis negative x minus 1 right parenthesis squared

g(x)=(−x+1)2
𝑔
(
𝑥
)
=
(
−
𝑥
+
1
)
2

g left parenthesis x right parenthesis equals left parenthesis negative x plus 1 right parenthesis squared

g(x)=−x2+1

Answer 1

g(x) = −(x + 1)^2

Reason: reflecting over the x-axis multiplies the function values by −1, so g(x) = −f(x) = −(x + 1)^2.