# If a function y = |x| has shifted 4 units left and 2 units up, the equation for the new function is: a) y = |x+4| - 2 b) y = |x+4| + 2 c) y = |x-4| - 2 d) y = |x-4| + 2

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Give the equation if f(x)=|x| has been translated 4 units left and 2 units up:

f(x)=|x-h|+k will be translated h units left/right and k units up/down.

So the equation will be y=|x+4|+2

The answer is B.

The graph of y=|x| in black and y=|x+4|+2 in red: