Question

Reflections as Functions Quick Check 3 of 53 of 5 Items Question The function f(x)=(x+1)2 is reflected over the x-axis to create g(x) . Identify the equation for g(x) .(1 point) Responses g(x)=−(x+1)2 g left parenthesis x right parenthesis equals negative left parenthesis x plus 1 right parenthesis squared g(x)=−x2+1 g left parenthesis x right parenthesis equals negative x squared plus 1 g(x)=(−x−1)2 g left parenthesis x right parenthesis equals left parenthesis negative x minus 1 right parenthesis squared g(x)=(−x+1)2 g left parenthesis x right parenthesis equals left parenthesis negative x plus 1 right parenthesis squared Skip to navigation page 14 of 14

Answer 1

To reflect the function $f(x)=(x+1{)}^2$ over the x-axis, we need to multiply the entire function by -1. This transformation changes the sign of the output values of the function.

Therefore, the reflected function $g(x)$ will be:

$$g(x)=-(x+1{)}^2$$

Among the response options, this corresponds to:

$$g(x)=-(x+1{)}^2$$

So, the correct answer is:

g(x) = −(x + 1)².