document.write( "Question 1112426: if f(x)=3 tan 2x, state the following.
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Algebra.Com's Answer #727461 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor's answer is correct about the period, but\r\n" );
document.write( "incorrect about the vertical asymptotes.\r\n" );
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document.write( "The period of \r\n" );
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document.write( "\"f%28x%29\"\"%22%22=%22%22\"\"a%2Atan%28bx%29\"\r\n" );
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document.write( "is \"pi%2Fb\"\r\n" );
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document.write( "and has vertical asymptotes wherever \r\n" );
document.write( "bx is an odd multiple of \"pi%2F2\"\r\n" );
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document.write( "Therefore the period of\r\n" );
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document.write( "\"f%28x%29\"\"%22%22=%22%22\"\"3tan%282x%29\"\r\n" );
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document.write( "is \"pi%2F2\"\r\n" );
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document.write( "and has vertical asymptotes wherever \r\n" );
document.write( "2x is an odd multiple of \"pi%2F2\"\r\n" );
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document.write( "Odd numbers are represented by 2n-1, so \r\n" );
document.write( "between -p and +p,\r\n" );
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document.write( "\"2x+=+%282n-1%29expr%28pi%2F2%29\"\r\n" );
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document.write( "\"x=expr%28%282n-1%29%2F4%29pi%0D%0A%0D%0A%7B%7B%7B-pi%3C=expr%28%282n-1%29%2F4%29pi%3C=pi\"\r\n" );
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document.write( "Multiplying through by 4\r\n" );
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document.write( "\"-4pi%3C=%282n-1%29pi%3C=4pi\"\r\n" );
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document.write( "Dividing all three sides by p\r\n" );
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document.write( "\"-4%3C=2n-1%3C=4\"\r\n" );
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document.write( "Adding 1 to all three sides:\r\n" );
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document.write( "\"-3%3C=2n%3C=5\"\r\n" );
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document.write( "Dividing all three sides by 2\r\n" );
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document.write( "\"-3%2F2%3C=n%3C=5%2F2\"\r\n" );
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document.write( "And since n is an integer, n=-1,0,1,2\r\n" );
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document.write( "So when n=-1, (2n-1)pi/2 = -3p/4\r\n" );
document.write( "And when n=1, (2n-1)pi/2 = -p/4\r\n" );
document.write( "And when n=1, (2n-1)pi/2 = p/4\r\n" );
document.write( "And when n=1, (2n-1)pi/2 = 3p/4\r\n" );
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document.write( "So in the interval (-p,p),\r\n" );
document.write( "the graph continues through 4 periods, and there are 4 vertical \r\n" );
document.write( "asymptotes at: \r\n" );
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document.write( "x = -3p/4, approximately -2.4\r\n" );
document.write( "x = -p/4, approximately -0.8\r\n" );
document.write( "x = p/4, approximately 0.8\r\n" );
document.write( "x = 3p/4, approximately 2.4\r\n" );
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document.write( "the 4 green lines are the 4 vertical asymptotes:\r\n" );
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document.write( "Edwin
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