# Math Help - Function sign

1. ## Function sign

What happens to a function when - is in front?

-f(x)

2. Nothing. The function remains the same.

However, if we graph a new function, -f(x), we'll find that it's simply f(x) flipped across the x-axis.

3. you can visualize it like this

$f(x)$ yields the coordinates $(x,y)$ and $-f(x)$ yeilds the coordinaes $(x,-y)$. So every $y$ value in the $f(x)$ is the mirror image of the $-f(x)$ outputs. That's why we say the $-f(x)$ is the reflection through the $x-axis$ of $f(x)$. Make sense?

4. "f(x)" is just another name for "y". If you take a graph's y-values and change their signs, then you're moving the points to the opposite side of the x-axis. In other words, you're flipping the graph upside-down.