What happens to a function when - is in front?

-f(x)

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- May 18th 2009, 09:35 AManon_404Function sign
What happens to a function when - is in front?

-f(x) - May 18th 2009, 09:41 AMderfleurer
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 AMVonNemo19
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 thethrough the $\displaystyle x-axis$ of $\displaystyle f(x)$. Make sense?*reflection* - May 18th 2009, 11:40 AMstapel
"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)