Answer
$f(x)=-|x-4|+3$
Work Step by Step
Given the standard function, $
f(x)=|x|
$, the equation of the graph that is reflected about the $x-$axis will have a negative multiplier in the $y-$variable. Hence, the equation becomes
\begin{array}{l}\require{cancel}
-f(x)=|x|
\\\\
f(x)=-|x|
.\end{array}
Given the standard function, $
f(x)=-|x|
$, the equation of the graph that shifts to the right will have a negative constant added to the $x-$variable. Hence, a shift of $4$ units to the right will have the equation,
\begin{array}{l}\require{cancel}
f(x)=-|x-4|
.\end{array}
Given the standard function, $
f(x)=-|x-4|
$, the equation of the graph that shifts upward will have a positive constant added to the equation. Hence, a shift of $3$ units up will have the equation,
\begin{array}{l}\require{cancel}
f(x)=-|x-4|+3
.\end{array}
