reflections of functions

Question

find g(x) where g(x) is the reflection across the x axis of f(x) = - 6x - 2

Answer 1

Change to a "standard transformation form":

f(x) = -6(x + 1/3)

Note that this is the y = x parent transformed by moving left by 1/3 and stretched vertically by a factor of 6

Reflect it across the x-axis:

g(x) = -(-6(x + 1/3))

Simplify:

g(x) = 6(x + 1/3)

g(x) = 6x + 2