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

The reflection over the x-axis is done by changing \( f(x) \) to \( -f(x) \):

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

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

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

Therefore, the correct response is:

g(x) = −(x + 1)².