# Function sign

• May 18th 2009, 09:35 AM
anon_404
Function sign
What happens to a function when - is in front?

-f(x)
• May 18th 2009, 09:41 AM
derfleurer
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.
• May 18th 2009, 10:11 AM
VonNemo19
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?
• May 18th 2009, 11:40 AM
stapel
"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)