Function sign

What happens to a function when - is in front?

-f(x)

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.

you can visualize it like this

yields the coordinates and yeilds the coordinaes . So every value in the is the mirror image of the outputs. That's why we say the is the reflection through the of . Make sense?

"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. (Wink)