What is the range of 3sin(2x-pi/4)+1 ?

The range of 3sin(2x-pi/4)+1 is -2<= f(x)<= 4

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range of 3sin(2x-pi/4)+1

range

3 sin (2 x - \frac{π}{4}) + 1

- 2 \leq f (x) \leq 4

Interval Notation

[- 2, 4]

Solution steps

The range of the basic

sin

function is

- 1 \leq sin (2 x - \frac{π}{4}) \leq 1

- 1 \leq sin (2 x - \frac{π}{4}) \leq 1

Multiply the edges of the range by:

3

- 3 \leq 3 sin (2 x - \frac{π}{4}) \leq 3

Add to the edges of the range:

1

- 2 \leq 3 sin (2 x - \frac{π}{4}) + 1 \leq 4

Therefore the range is

- 2 \leq f (x) \leq 4

What is the range of 3sin(2x-pi/4)+1 ?
The range of 3sin(2x-pi/4)+1 is -2<= f(x)<= 4