ANSWER
[tex]g(x) = \sin(x +4) - 4[/tex]
EXPLANATION
The basic sine function is
[tex]f(x) = \sin(x) [/tex]
The transformed sine function has equation
[tex]g(x) = a \sin(bx +c ) + d[/tex]
where a=1 is the amplitude
2π/b=2π is the period
c/b= 4 is the horizontal shift 4 units left.
d=-4 is a downward vertical shift of 4 units.
The required sine function is:
[tex]g(x) = \sin(x +4) - 4[/tex]
