Am i correct? which of the following describes how to translate the graph of y = |x| to obtain the graph of y = |x + 1| - 2? shift right 1 and down 2 shift left 1 and down 2 < < < shift right 1 and up 2,

You are actually incorrect, as setting x=0 shows that the shifted graph needs to hit the y-axis at -2 (a downshift of 2). Similarly setting y=0, we find that x then becomes -1, since the absolute value of x +1 =0 implies that x=-1. So the correct answer is actually a shift down of 2 and left of 1.