i have attched the problem which i am having trouble with
Hello, carlasader!
Exactly where is your difficulty?
. . Are you at all familiar with "translations"?
$\displaystyle a)\;\;y \:=\:f(\text{-}x)$
Replacing $\displaystyle x$ with $\displaystyle \text{-}x$ reflects the graph across the $\displaystyle y$-axis.
. . The graph is a left/right mirror-image.
$\displaystyle b)\;\;y = -f(x)$
Replacing $\displaystyle f(x)$ with $\displaystyle \text{-}f(x)$ reflects the graph across the $\displaystyle x$-axis.
. . The graph is an up/down mirror-image.
$\displaystyle c)\;\;y = f(|x|)$
Replacing $\displaystyle x$ with $\displaystyle |x|$ reflects the right half of the graph
. . onto the left side.