Answer
$f(x)=\dfrac{1}{2}|x+1|+3$
Work Step by Step
Given the standard function, $
f(x)=|x|
$, the equation of the graph that shrinks vertically has a multiplier of $\dfrac{1}{c}$ on the $y-$variable. Hence, a vertical shrinking of a factor of $\dfrac{1}{2}$ units has the equation,
\begin{array}{l}\require{cancel}
\dfrac{1}{1/2}f(x)=|x|
\\\\
2f(x)=|x|
\\\\
f(x)=\dfrac{1}{2}|x|
.\end{array}
Given the function, $
f(x)=\dfrac{1}{2}|x|
$, the equation of the graph that shifts to the left has a positive constant added to the $x-$variable. Hence, a shift of $1$ unit to the left has the equation
\begin{array}{l}\require{cancel}
f(x)=\dfrac{1}{2}|x+1|
.\end{array}
Given the function, $
f(x)=\dfrac{1}{2}|x+1|
$, the equation of the graph that shifts up has a positive constant added to the equation. Hence, a shift of $3$ units up has the equation
\begin{array}{l}\require{cancel}
f(x)=\dfrac{1}{2}|x+1|+3
.\end{array}
