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

Transcript text: The function $f(x)=(x+1)^{2}$ is reflected over the $y$-axis to create $\mathrm{g}(\mathrm{x})$. Identify the equation for $\mathrm{g}(\mathrm{x})$. (1 point) $g(x)=-x^{2}+1$ $g(x)=-(x+1)^{2}$ $g(x)=(-x-1)^{2}$ $g(x)=(-x+1)^{2}$

Solution

Solution Steps

To reflect a function over the y-axis, replace $ x $ with $ -x $ in the function's equation. For the given function $ f(x) = (x+1)^2 $, substitute $ -x $ for $ x $ to find the equation for $ g(x) $.

Step 1: Reflect the Function Over the $ y $-Axis

To reflect the function $ f(x) = (x+1)^2 $ over the $ y $-axis, we substitute $ -x $ for $ x $. This gives us the new function: \[ g(x) = (-x + 1)^2 \]

Step 2: Expand the Reflected Function

Next, we expand the expression $ (-x + 1)^2 $: \[ g(x) = (-x + 1)^2 = (-x + 1)(-x + 1) = x^2 - 2x + 1 \]