What is the range of-5cos(x/3+pi/2)-4 ?

The range of-5cos(x/3+pi/2)-4 is -9<= f(x)<= 1

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range of-5cos(x/3+pi/2)-4

range

- 5 cos (\frac{x}{3} + \frac{π}{2}) - 4

- 9 \leq f (x) \leq 1

Interval Notation

[- 9, 1]

Solution steps

The range of the basic

cos

function is

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

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

Multiply the edges of the range by:

- 5

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

Add to the edges of the range:

- 4

- 9 \leq - 5 cos (\frac{x}{3} + \frac{π}{2}) - 4 \leq 1

Therefore the range is

- 9 \leq f (x) \leq 1

f (x) = - 3 x + 10

3 x - y = 7

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

f (x) = \frac{- x + 17}{7}

f (x) = \frac{25}{x - 58} - 23

What is the range of-5cos(x/3+pi/2)-4 ?
The range of-5cos(x/3+pi/2)-4 is -9<= f(x)<= 1