reflections of functions

Question

find g(x), where g(x) is the reflection across the x axis of f(x)= -10x-9

Answer 1

What does it actually mean to reflect a function across the x-axis? It means that each point (x, y) on the original plot is now (x, -y). If this isn't clear to you, draw some sketches and convince yourself of this fact.

Equivalently, this means (x, f(x)) -> (x, -f(x)). Your new function g(x) is simply - f(x). Applying this, we have g(x) = 10x + 9.