what are the coordinates of that center of a circle if the endpoints of its diameter are a(8,-4) and b(-3,2)?

You need to add 8 and -3 together to get 5 and divide 5 by 2 to get 2.5
That is the x coordinate
You then need to add 2 and -4 together to get -2 and divide by 2 to get -1
This is the y coordinate
(2.5,-1)

Answers: the graph is translated down 1 unit and the domain and range of g(x) is the same as the domain and range of f(x).