Question

The function f(x)=x2−1
𝑓
(
𝑥
)
=
𝑥
2
−
1
is reflected over the y-axis. Choose the equation that correctly identifies g(x)
𝑔
(
𝑥
)
.(1 point)
Responses

g(x)=x2+1
𝑔
(
𝑥
)
=
𝑥
2
+
1
g left parenthesis x right parenthesis equals x squared plus 1

g(x)=−x2−2
𝑔
(
𝑥
)
=
−
𝑥
2
−
2
g left parenthesis x right parenthesis equals negative x squared minus 2

g(x)=−x2+1
𝑔
(
𝑥
)
=
−
𝑥
2
+
1
g left parenthesis x right parenthesis equals negative x squared plus 1

g(x)=x2−1

Answer 1

g(x) = x^2 − 1

Reason: reflection over the y-axis gives g(x) = f(−x) = (−x)^2 − 1 = x^2 − 1, so the function is unchanged (even).