Start with the base graph: y = |x|
Translate the graph one unit to the right: y = |x - 1|
---We use a minus/negative/subtraction sign when dealing with horizontal translations because it is the opposite of the way we want to go. If the translation occurs within parenthesis/absolute value bars, we always do the opposite of what we think we should.
Translate the graph one unit down: y = |x - 1| - 1
---If the translation occurs to the y-value/vertically, we use the expected operation/sign. If the translation occurs outside of parenthesis, we use the same operation/sign as the translation (+ for up, - for down).
Answer: y = |x - 1| - 1
Hope this helps!