To write the formula for the function obtained when the graph of [tex]\( f(x) = |x| \)[/tex] is shifted down 3 units and to the right 1 unit, let's follow the steps provided:
1. Original Function: The given function is [tex]\( f(x) = |x| \)[/tex].
2. Shifting Down 3 Units: When a function is shifted down by 3 units, we subtract 3 from the function. Thus, the function becomes:
[tex]\[
f(x) = |x| - 3
\][/tex]
3. Shifting to the Right 1 Unit: When a function is shifted to the right by 1 unit, we replace [tex]\( x \)[/tex] with [tex]\( (x - 1) \)[/tex] in the function. Applying this shift to our current function:
[tex]\[
f(x) = |x - 1| - 3
\][/tex]
So, the formula for the function obtained after shifting the graph of [tex]\( f(x) = |x| \)[/tex] down 3 units and to the right 1 unit is:
[tex]\[
f(x) = |x - 1| - 3
\][/tex]
