Question

which of the following functions represents a reflection of the function graphed over the x - axis? (1 point)
$y = -|x + 1|$
$y = |-x|$
$y = -|x - 1|$
$y = |x - 1|$

Explanation:

Step1: Recall reflection rule

When a function $y = f(x)$ is reflected over the x - axis, the transformation is $y=-f(x)$.

Step2: Identify original function

The original function is $f(x)=|x + 1|$.

Step3: Apply reflection rule

The reflected function over the x - axis is $y=-|x + 1|$.

Answer:

$y = -|x + 1|$ (corresponding to the first option in the multiple - choice list)