Answer
(a) D: $[0,4]$, R: $[-3,0]$.
(b) D: $[-4,0]$, R: $[0,3]$.
(c) D: $[-4,0]$, R: $[0,3]$.
(d) D: $[-4,0]$, R: $[1,4]$.
(e) D: $[2,6]$, R: $[-3,0]$.
(f) D: $[-2,2]$, R: $[-3,0]$.
(g) D: $[1,5]$, R: $[-3,0]$.
(h) D: $[0,4]$, R: $0,3]$.
Work Step by Step
See the graph. The original domain is $[-4,0]$ and the range is $[-3,0]$. Shift the domain and range according to the operations on the function:
(a) For $g(-t)$, the new domain is $[0,4]$ and the new range is $[-3,0]$.
(b) For $-g(t)$, the new domain is $[-4,0]$ and the new range is $[0,3]$.
(c) For $g(t)+3$, the new domain is $[-4,0]$ and the new range is $[0,3]$.
(d) For $1-g(t)$, the new domain is $[-4,0]$ and the new range is $[1,4]$.
(e) For $g(-t+2)$, the new domain is $[2,6]$ and the new range is $[-3,0]$.
(f) For $g(t-2)$, the new domain is $[-2,2]$ and the new range is $[-3,0]$.
(g) For $g(1-t)$, the new domain is $[1,5]$ and the new range is $[-3,0]$.
(h) For $-g(t-4)$, the new domain is $[0,4]$ and the new range is $0,3]$.
