Answer:
[tex]g(x)=|x+4|+2[/tex].
Step-by-step explanation:
The given function is
[tex]f(x)=|x|[/tex]
The translation is defined as
[tex]g(x)=f(x+a)+b[/tex] .... (1)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
It is given that f(x) shifts 4 units left and 2 units up. So,
[tex]a=4\text{ and }b=2[/tex]
Substitute a=4 and b=2 in equation (1).
[tex]g(x)=f(x+4)+2[/tex]
[tex]g(x)=|x+4|+2[/tex] [tex][\because f(x)=|x|][/tex]
Therefore, the new function is [tex]g(x)=|x+4|+2[/tex].
