Question

if the function y= -3 cos(2x) has been translated 2 units up, then what is the new range of the function?

Answer 1

Range: -1 ≤ y ≤ 5

Explanation:

Translations

For a > 0

`f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}`

`f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}`

`f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}`

`f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}`

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