In the diagram below, assume $\backslash ($ c$=3\backslash ).$

In the following parts, do not use parentheses as function inputs. For instance, if you want to input either $\backslash ($ f$($x$)\backslash )$ or $\backslash ($ f$($y$)\backslash ),$ input $\backslash ($ f $\backslash )$ instead.

$($a$)$ Write an expression for the length of the red $($dotted$)$ line segment.

$($b$)$ Write an expression for the length of the blue $($dash$-$dotted$)$ line segment.

$($c$)$ In the previous parts, were $\backslash ($ f $\backslash )$ and $\backslash ($ g $\backslash )$ functions of $\backslash ($ x $\backslash )$ or $\backslash ($ y $\backslash )?$