Question

question 7
the absolute value function ( y = | -x - 3 | + 4 ) is graphed. if a reflection over the ( x )-axis is performed on the given function, what will the new equation be?
( \bigcirc ) ( y = | -x - 3 | + 4 )
( \bigcirc ) ( y = -| -x - 3 | + 4 )
( \bigcirc ) ( y = | -x - 3 | - 4 )
( \bigcirc ) ( y = | x - 3 | + 4 )

Explanation:

Step1: Recall reflection rule over x-axis

To reflect a function $y=f(x)$ over the x-axis, the new function is $y=-f(x)$.

Step2: Apply rule to given function

Given $f(x)=|-x-3|+4$, the reflected function is $y=-(|-x-3|+4)$

Step3: Simplify the expression

$y=-|-x-3|-4$ is incorrect; expand the negative sign: $y=-|-x-3|+4$

Answer:

$y=-|-x-3|+4$