Sketch two complete periods of the graph of y cot1x Label t

Sketch two complete periods of the graph of y = -cot(1/x). Label the x-intercepts with ordered pairs. Isabel each asymptote with its equation. What is the domain of this function?

Solution

y=-cot(1x/2)

This is of the form y=Acot(BX -C)

where period =pi/B

In the given function

period=pi/1/2=2pi

To find the vertical asymptotes,we have to set Bx - C to 0 and pi

x/2=0       and     x/2=pi

x=0          and       x=2pi