# Math Help - sketch the curve

1. ## sketch the curve

i have attched the problem which i am having trouble with

. . Are you at all familiar with "translations"?

$a)\;\;y \:=\:f(\text{-}x)$

Replacing $x$ with $\text{-}x$ reflects the graph across the $y$-axis.
. . The graph is a left/right mirror-image.

$b)\;\;y = -f(x)$

Replacing $f(x)$ with $\text{-}f(x)$ reflects the graph across the $x$-axis.
. . The graph is an up/down mirror-image.

$c)\;\;y = f(|x|)$

Replacing $x$ with $|x|$ reflects the right half of the graph
. . onto the left side.