The two functions are
y= f(x), ------------(1)
g(x)= f(x+2)---------(2)
⇒Consider a point (a,b) on the curve.It will satisfy (1).
b = f(a)
Now the point a is translated by 2 units right in horizontal direction and there is no vertical shift.
Coordinate of new point = (a+2,b)
Putting the value of new coordinate in equation (1), we get
b = f(a+2)
which gives equation (2), which is
g(x)= f(x+2)
Option (3) is correct,which is, the graph of g(x) is graph of f(x) translated 2 units right.