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)

Question

Responses

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

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

Answer 1

To reflect the function \( f(x) = (x+1)^2 \) over the x-axis, we need to negate the entire function. This means we take:

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

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

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

So the correct response is:

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

This matches with the option:

g(x)=−(x+1)².