What is the range of y=3-2sin(3x-pi) ?

The range of y=3-2sin(3x-pi) is 1<= f(x)<= 5

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range of y=3-2sin(3x-pi)

range

1 \leq f (x) \leq 5

Interval Notation

[1, 5]

Solution steps

The range of the basic

sin

function is

- 1 \leq sin (3 x - π) \leq 1

- 1 \leq sin (3 x - π) \leq 1

Multiply the edges of the range by:

- 2

- 2 \leq - 2 sin (3 x - π) \leq 2

Add to the edges of the range:

3

1 \leq - 2 sin (3 x - π) + 3 \leq 5

Therefore the range is

1 \leq f (x) \leq 5

What is the range of y=3-2sin(3x-pi) ?
The range of y=3-2sin(3x-pi) is 1<= f(x)<= 5