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

The range of 3-4sin(2/3 (x-1)) is -1<= f(x)<= 7

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

range

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

- 1 \leq f (x) \leq 7

Interval Notation

[- 1, 7]

Solution steps

The range of the basic

sin

function is

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

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

Multiply the edges of the range by:

- 4

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

Add to the edges of the range:

3

- 1 \leq - 4 sin (\frac{2}{3} (x - 1)) + 3 \leq 7

Therefore the range is

- 1 \leq f (x) \leq 7

in t erce pt s x - 3 x - 28

r an g e \frac{7 x}{5 x - 6}

d o main f (x) = 2 x + 1

e x t re m e \frac{x ^{3}}{x ^{2} - 4}

p a r i t y f (x) = x^{4} - 2 x^{2}

What is the range of 3-4sin(2/3 (x-1)) ?
The range of 3-4sin(2/3 (x-1)) is -1<= f(x)<= 7