Sketch two periods

Question

Sketch two periods of the function f(x) = tan(2x-3π), without using a graphing calculator. Make it clear by labeling the axes and key points on the graph.

Answer 1

One copy of the graph of y = tanx is traced out when -π/2 < x < π/2.

So, for y = tan(2x - 3π), if -π/2 < 2x - 3π < π/2, then 5π/2 < 2x < 7π/2. So 5π/4 < x < 7π/4

One copy from 5π/4 to 7π/4 and another from 7π/4 to 9π/4.