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

Question

a. g (x) = (-x-1)^2
b. g (x) = - x^2 + 1
c. g (x) = - (-x+1)^2
d. g (x) = - (x+1)^2

Answer 1

To reflect the function \( f(x) = (x+1)^2 \) over the x-axis, you need to take the negative of the entire function.

The reflection is given by:

\[ g(x) = -f(x) \]

Substituting \( f(x) \):

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

This simplifies to:

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

Thus, the correct answer is:

d. \( g(x) = - (x+1)^2 \).