The required function after shifting its origin will be g(x) = |x + 5| - 4.
What is Shifting of Origin?
To shift the coordinates of origin to (h,k): Replace x by (x-h) and y by (y-k) in the given equation and get the new equation.
Here, given function f(x) = |x|
or y = |x|
Now, Shift 5 units to the left. x replaces with x - (-5) = x + 5
Shift 4 units down, y replaces with y -(-4) = y + 4
Now equation after shifting ,
y - k = | x - h|
y = |x -h| + k
y = |x - (-5)| +(-4)
g(x) = |x+5|-4
Thus, The required function after shifting its origin will be g(x) = |x + 5| - 4.
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