Write the equations after translating the graph of y=|2x|-1:

one unit up

f (x + n) - translate n units left

f (x - n) - translate n units right

f (x) + n - translate n units up

f (x) - n - translate n units down

We translate the graph 1 unit up, therefore we have f (x) + 1. Substitute to the equation of function f (x) = |2x| - 1

f (x) + 1 = |2x| - 1 + 1 = |2x| = 2|x|