Graph g (x) = 2+|x| and it's parent functions

The parent function is ...

... f (x) = |x|

This is the absolute value function, equal x when x ≥ 0, and equal to - x when x < 0. Its graph has the shape of a V with the vertex at the origin and "legs" of slope ±1.

The function g (x) is the same function with 2 added. The addition of 2 moves every value of f (x) up 2 units, so translates the whole graph upward by 2 units.