Question

I need to state the period and 2 consecutive asymptotes on the graph for the following questions.

1: y = -3 tan pi*x
period: pi (?)
asymptotes: ?

2: y = 2 sec 4x
period: ?
asymptotes: ?

3: y = csc (x/3)
period: ?
asymptotes: ?

4: y = 3 cot (pi*x/2)
period: ?
asymptotes: ?


If possible, I'd love some explanation/clarification for the answers as well so I can understand it better... thanks!

Answer 1

1: y = -3 tan pi*x
period: pi (?)
asymptotes: ?
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Well, I will help with the first one. Then you better try to use a similar approach on the rest
y = -3 sin pi x/ cos pi x
this repeats when pi x = pi
or period = 1 pi
It gets undefined when cos pi x = 0
or pi x = pi/2 which is x = 1/2
then pi x = 3 pi/2 which is x = 3/2