Answer:
Range: -1 ≤ y ≤ 5
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function: y = -3 cos(2x)
Translated 2 units up: y = -3 cos(2x) + 2
Range of y = cos(2x) : -1 ≤ y ≤ 1
Range of Parent function y = -3 cos(2x) : -3 ≤ y ≤ 3
Range of new function y = -3 cos(2x) + 2: -1 ≤ y ≤ 5
