Answer:
The correct option is 2.
Step-by-step explanation:
The parent absolute function is
[tex]f(x)=|x|[/tex]
The graph of this function is V-shaped and the vertex of this function is origin.
The transformation is defined as
[tex]g(x)=|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.
From the given graph it is clear that the function shifts 2.5 units up. It means a=0 and b=2.5.
Substitute a=0 and b=2.5 in equation (1).
[tex]g(x)=|x+0|+2.5[/tex]
[tex]g(x)=|x|+2.5[/tex]
The required function is g(x)=|x|+2.5. Therefore the correct option is 2.
