Answer:
[tex]g(x)=\frac{1}{2}sinx -3[/tex]
Step-by-step explanation:
The original function is f(x) = sinx
This function is in the form of f(x) = asin(bx + c) + d
Here amplitude a = 1, c = 0 and vertical shift is d = 0.
when this function is transformed into a new function by using instructions as
1) compressed vertically by a factor of 1/2 that means amplitude of the sine function was compressed by a scale factor of 1/2 and the new function will have amplitude a = 1/2.
2) shifting of sine function by 3 units down means d = -3
So the new function will be
g(x) = (1/2) sin(x) - 3
