Answer :
For a right shift of 5, you replace x with x-5.
For a down shift of 4, you replace f(x) with f(x)-4.
The new function is ...
|x -5| -4
For a down shift of 4, you replace f(x) with f(x)-4.
The new function is ...
|x -5| -4

Answer:
The equation of the transformed function is:
[tex]g(x)=|x-5|-4[/tex]
Step-by-step explanation:
We are given a absolute value parent function f(x) by:
[tex]f(x)=|x|[/tex]
Now we have to apply some transformation to this parent function in order to get the transformed function.
The transformations that are applied are:
Shift 5 units to the right. Shift 4 units down.
We know that:
The shift of the parent function a units to the left or right is given by:
[tex]g(x)=f(x+a)[/tex]
If a>0 then the shift is a units to the left
and if a<0 then the shift is a units to the right.
Also, the shift of k units to the left and right of some parent function f(x) is given by:
[tex]g(x)=f(x)+k[/tex]
if k<0 then the shift is downward.
and if k>0 then the shift is upward.
So, here the equation of the transformed function is:
[tex]g(x)=|x-5|-4[/tex]
