Question

find g(x), where g(x) is the reflection across the x-axis of f(x) = 7|x - 5| + 6.\
\
\\(g(x) = -7|x - 5| + 6\\)\
\\(g(x) = 7|x - 5| + 6\\)\
\\(g(x) = 7|x + 5| + 6\\)\
\\(g(x) = -7|x - 5| - 6\\)

Explanation:

Step1: Recall x-axis reflection rule

Reflecting $f(x)$ over x-axis gives $g(x) = -f(x)$.

Step2: Substitute $f(x)$ into the rule

$g(x) = -(7|x - 5| + 6)$

Step3: Distribute the negative sign

$g(x) = -7|x - 5| - 6$

Answer:

g(x) = -7|x - 5| - 6