What is the range of f(x)=-2sin(x/2-pi/3)+5 ?

The range of f(x)=-2sin(x/2-pi/3)+5 is 3<= f(x)<= 7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

range of f(x)=-2sin(x/2-pi/3)+5

range

f (x) = - 2 sin (\frac{x}{2} - \frac{π}{3}) + 5

3 \leq f (x) \leq 7

Interval Notation

[3, 7]

Solution steps

The range of the basic

sin

function is

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

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

Multiply the edges of the range by:

- 2

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

Add to the edges of the range:

5

3 \leq - 2 sin (\frac{x}{2} - \frac{π}{3}) + 5 \leq 7

Therefore the range is

3 \leq f (x) \leq 7

What is the range of f(x)=-2sin(x/2-pi/3)+5 ?
The range of f(x)=-2sin(x/2-pi/3)+5 is 3<= f(x)<= 7