What are the asymptotes of y=-3/2 tan (x + pi/2)

Question

What are two consecutive asymptotes between those aysmptotes how would you plot a point that intersects the x -axis, a point to its left, and a point to its right?

*what are the points and asymptotes*

Answer 1

This graph slides the graph of y = tan x, pi/2 units to the left.

There would be vertical asymptotes at x=0 and x = pi

At x = pi/2 you would be evaluating tan(pi/2 + pi/2 ) = tan(pi) = 0 (pt cross x axis)

Two easy points to graph would be to find the x's that causes x + pi/2 to be 3pi/4 and 5pi/4

So

When x = pi/4 , pi/4 + pi/2 = 3pi/4 thus tan(3pi/4) = -1 times -3/2 would = 3/2

When x= 3pi/4 , pi/4 + pi/2 = 5pi/4 thus tan(5pi.4) = 1 times -3/2 would be -3/2

Three points

(pi/4, 3/2) (pi/2,0) (3pi/4, -3/2)