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