What is the range of-8csc(pi/3 x) ?

The range of-8csc(pi/3 x) is f(x) = 8

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range of-8csc(pi/3 x)

range

- 8 csc (\frac{π}{3} x)

f (x) \leq - 8 or f (x) \geq 8

Interval Notation

(- \infty, - 8] \cup [8, \infty)

Solution steps

The range of the basic

csc

function is

csc (\frac{π}{3} x) \leq - 1 or csc (\frac{π}{3} x) \geq 1

csc (\frac{π}{3} x) \leq - 1 or csc (\frac{π}{3} x) \geq 1

Multiply the edges of the range by:

- 8

- 8 csc (\frac{π}{3} x) \leq - 8 or - 8 csc (\frac{π}{3} x) \geq 8

Therefore the range is

f (x) \leq - 8 or f (x) \geq 8

d o main f (x) = \frac{- 6}{x + 3}

in v erse f (x) = 0.9 (x - 7) - 8

d o main 2^{x} - 7

a sy m pt o t es f (x) = \frac{1}{x - 5} + 3

a sy m pt o t es f (x) = \frac{x ^{2} - 9}{x + 1}

What is the range of-8csc(pi/3 x) ?
The range of-8csc(pi/3 x) is f(x)<=-8\lor f(x)>= 8