The function f(x) = (x + 1)^2 is reflected over the x-axis to create g(x). Identify the equation for g(x).

Answer 1

To reflect the function \( f(x) = (x + 1)^2 \) over the x-axis, we need to multiply the entire function by \(-1\).

The original function is:

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

To find \( g(x) \), which is the reflection of \( f(x) \) over the x-axis, we have:

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

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

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

This means that the equation for \( g(x) \) after the reflection is:

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