Question

. The following transformations y=3f(1/2x-2pi)-1 were applied to the parent function f(x)=csc(x). Graph the transformed function for the interval − 4π ≤ 𝑥 ≤ 4π. On your graph, label the asymptotes, local max/min, and number each axis. Use mapping notation to show your work for a minimum of 5 key points

Answer 1

you know that csc(x) has turning points at all odd multiples of pi/2
so, csc(1/2 x - 2pi) has turning points where x/2 - 2pi is an odd multiple of pi/2. They occur with period pi, and are at y = 3-1 and -3-1
The asymptotes are midway between the turning points