tanx has a period of ##pi##, but since we have 2x here we need to divide it by 2 and get a period of ##pi/2##

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tanx has a period of ##pi##, but since we have 2x here we need to divide it by 2 and get a period of ##pi/2##. Since there is no coefficient in front of the tan the amplitude is 1.

So tan2x has vertical asymptote every ##pi/2##

Now graph it.

graph{tan(2x) [-10, 10, -5, 5]}