Answer:
The integer 4 represents the horizontal translation of f(x) to g(x).
Step-by-step explanation:
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.
From the given figure it is clear that the graph of f(x) horizontally shifts 4 units to the left. So, the value of a is 4 and the value of b is 0.
The translation for given function as
[tex]g(x)=f(x+4)+0[/tex]
Therefore, the integer 4 represents the horizontal translation of f(x) to g(x).
