Chapter 2 Linear Equations and Functions - 2.7 Use Absolute Value Functions and Transformations - 2.7 Exercises - Skill Practice - Page 127: 16

$y=|x-4|+3$.

The functions have the form $y=a|x-b|+c$ where $(b,c)$ is the vertex of the function. Hence, because the vertex is at $(4,3)$, $y=a|x-4|+3$. Since $(5,4)$ is on the function, plugging in the values we get: $4=a|5-4|+3\\4=a+3\\a=1$. Thus $y=|x-4|+3$.