Question

y= -cot (3x-2pi/3) + 2
graph and find assymptotes

Answer 1

-2cot*

Answer 2

-2cot(3x-2pi/3) + 2

the -2 just scales the height, so it does not affect the asymptotes, which are all vertical

similarly, the +2 does not affect them.

So, now you are left with

cot(3x-2π/3)

Now, cot(x) has asymptotes at all multiples of π

you have cot(3(x-2π/9))

so, the graph has been shifted right by 2π/9 and now has period π/3. So, its asymptotes are now at

2π/9 + kπ/3 for all integer k.
That is, 2π/9, 5π/9, 8π/9, ...

Answer 3

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