Write a formula for the function obtained when the graph of f(x) = | x | is shifted down 3 units and to the right 1 unit

Question

g(x) = |x-1| - 3
|x+1| + 3
|x+3| - 1
|x+1| - 3

3
|x+1| +3

Answer 1

To obtain the function \( g(x) \) from the original function \( f(x) = |x| \) by shifting it down 3 units and to the right 1 unit, you can follow these steps:

1. Shift to the right by 1 unit:
   This means replacing \( x \) with \( x - 1 \). So, we have: \[ f(x) = |x| \quad \Rightarrow \quad f(x - 1) = |x - 1| \]

2. Shift down by 3 units:
   This means subtracting 3 from the entire function. So now we have: \[ g(x) = |x - 1| - 3 \]

Therefore, the correct function after shifting is: \[ g(x) = |x - 1| - 3 \]

Among the options given, this matches:

• \( g(x) = |x - 1| - 3 \)

This is the desired transformed function.