If the graph of y = |x| is translated so that the point (1, 1) is moved to (4, 1), what is the equation of the new graph?

(1, 1) is translated to (4, 1). The y coordinate has not changed, it means the graph has been shifted horizontally 3 units.

Let a be a positive number, The general rule of translation is that,

y=f(x-a) is y=f(x) shifted a units to the right

and

y=(x+a) is y=f(x) shifted a units to the left

so y=|x| shifted 3 units to the right is y=|x-3|

check:

 y=|x| : (x, |x|) for x=1 is (1, |1|)=(1, 1)
y=|x-3|: (x,|x-3|) for x=4 is (4,|4-3|)=(4, 1) 

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