Question

The function f(x)=(x+1)2 is reflected over the x-axis to create g(x) . Identify the equation for g(x) .(1 point) Responses 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 left parenthesis x right parenthesis equals left parenthesis negative x minus 1 right parenthesis squared g(x)=−x2+1 g left parenthesis x right parenthesis equals negative x squared plus 1 g(x)=(−x+1)2

Answer 1

To reflect the function \( f(x) = (x + 1)^2 \) over the x-axis, we take the original function and multiply it by -1.

So, to find \( g(x) \), we apply the transformation:

\[
g(x) = -f(x) = -((x + 1)^2)
\]

Thus, the equation for \( g(x) \) is:

\[
g(x) = -(x + 1)^2
\]

This corresponds to the first response option:

**g(x) = −(x + 1)²**.