Question

How do you find the domain & range for `3 Cot(2x)`?

Answer 1

Domain : `x in ( -oo, oo )`, sans `uarr` asymptoiic `darr` `x = k(pi/2)`,
`k = 0, +-1, +-2, +-3, ...`
Range: `y notin ( -1/2, 1/2 )`

Explanation:

`y = 3 cot 2x = 3 (cos (2x)/sin (2x)) in ( - oo. oo )`, ,

`x ne` zeros of the denominator `sin 2x`

`rArr x ne` an integer multiple of `(pi/2)`

The period

= the common period of `sin 2x and cos 2x = (2pi)/2 = pi`

See graph. revealing all these aspects:
graph{(y sin (2x) - 3 cos (2x) )= 0[ -10 10 -10 10]}