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

The range of 4sin(pi/3 x)+2 is -2<= f(x)<= 6

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

range

4 sin (\frac{π}{3} x) + 2

- 2 \leq f (x) \leq 6

Interval Notation

[- 2, 6]

Solution steps

The range of the basic

sin

function is

- 1 \leq sin (\frac{π}{3} x) \leq 1

- 1 \leq sin (\frac{π}{3} x) \leq 1

Multiply the edges of the range by:

4

- 4 \leq 4 sin (\frac{π}{3} x) \leq 4

Add to the edges of the range:

2

- 2 \leq 4 sin (\frac{π}{3} x) + 2 \leq 6

Therefore the range is

- 2 \leq f (x) \leq 6

4 sin (π x)

x^{3} - 7 x

\frac{- 5 x + 25}{9}

\frac{2 x + 6}{- 6 x + 3}

f (x) = x^{2} + 5

What is the range of 4sin(pi/3 x)+2 ?
The range of 4sin(pi/3 x)+2 is -2<= f(x)<= 6