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

Answer 1

To reflect the function \( f(x) = (x + 1)^2 \) over the x-axis, we take the negative of the entire function. Therefore, the new function \( g(x) \) can be expressed as:

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

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

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

Thus, the correct response from the options provided is:

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

Or equivalently, in the options given,

g(x) = - (x + 1)^2 (if that option exists in the format mentioned).