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

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

1 answer

To reflect the function \( f(x) = (x + 1)^2 \) over the y-axis, we replace \( x \) with \( -x \) in the function.

So, we calculate:

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

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

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

So the correct answer is:

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

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