Question

refer to the graph: if a reflection over the x - axis is performed, what will the equation of the function be?
options:
$y = | - x - 2|$
$y = - |x + 2|$
$y = | - x + 2|$
$y = - |x - 2|$

Explanation:

Step1: Identify original function

The vertex of the given V-shaped graph is at $(-3, 0)$, and it opens upward. The parent function of an absolute value graph is $y=|x-h|+k$, where $(h,k)$ is the vertex. Substituting $h=-3$, $k=0$, the original function is $y=|x+3|$.

Step2: Apply x-axis reflection rule

A reflection over the x-axis transforms a function $f(x)$ to $-f(x)$. Multiply the original function by $-1$:
$y = -|x+3|$

Answer:

$y=-|x+3|$