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)=−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 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)=(−x−1)2 g left parenthesis x right parenthesis equals left parenthesis negative x minus 1 right parenthesis squared
1 answer
To find the equation for \( g(x) \), which is the reflection of \( f(x) = (x+1)^2 \) over the x-axis, we need to negate the output of \( f(x) \).
This means that:
\[ g(x) = -f(x) = -((x+1)^2) \]
Thus, the equation for \( g(x) \) is:
\[ g(x) = -(x+1)^2 \]
Looking at the options provided, this corresponds to:
So the correct response is:
g(x) = −(x+1)²
