What happens to a function when - is in front?
-f(x)
you can visualize it like this
$\displaystyle f(x)$ yields the coordinates $\displaystyle (x,y)$ and $\displaystyle -f(x)$ yeilds the coordinaes $\displaystyle (x,-y)$. So every $\displaystyle y$ value in the $\displaystyle f(x)$ is the mirror image of the $\displaystyle -f(x)$ outputs. That's why we say the $\displaystyle -f(x)$ is the reflection through the $\displaystyle x-axis$ of $\displaystyle f(x)$. Make sense?