The function f(x)=(2−x)2+1 is reflected over the y-axis. Write the equation of its reflection, g(x).(1 point)

Question

Responses

g(x)=(x+2)2+1
g left parenthesis x right parenthesis equals left parenthesis x plus 2 right parenthesis squared plus 1

g(x)=(x−2)2−1
g left parenthesis x right parenthesis equals left parenthesis x minus 2 right parenthesis squared minus 1

g(x)=(x−2)2+1
g left parenthesis x right parenthesis equals left parenthesis x minus 2 right parenthesis squared plus 1

g(x)=(−2−x)2−1

Answer 1

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

Starting with the original function:

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

Now, replacing \( x \) with \( -x \):

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

Therefore, the equation of its reflection, \( g(x) \), is:

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

So the correct response is:

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