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