Question

help me out i will give 30 points

Answer 1

Transformation by translation can be obtained by the following rule:
g(x)=f(x-h)+k
where
h=translation to the right
k=translation up.

In the given example, the curve f(x) has been translated left by 8 units (h=-8) and up 3 units (k=3)

Therefore the transformation is
g(x)=f(x-(-8)+3=f(x+8)+3

If f(x)=-2^x  (as shown in image)
then
g(x)=f(x+8)+3=-2^(x+8)+3