document.write( "Question 628076: How do you determine the range of this function:
\n" ); document.write( "y = 2 + 2sec(2x) \n" ); document.write( "

Algebra.Com's Answer #395357 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "y = 2 + 2sec(2x)\r\n" );
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document.write( "The upper part of the range will be when the secant has the smallest\r\n" );
document.write( "positive value up to infinity.\r\n" );
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document.write( "The smallest positive value of the secant is 1\r\n" );
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document.write( "So the minimum of the upper part of the range of\r\n" );
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document.write( "y = 2 + 2sec(2x) is 2 + 2(1) = 2 + 2 = 4\r\n" );
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document.write( "So the upper part of the range is [4, )\r\n" );
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document.write( "The lower part of the range will be from negative infinity\r\n" );
document.write( "up to when the secant has the largest negative value.\r\n" );
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document.write( "The largest negative value of the secant is -1\r\n" );
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document.write( "So the maximum of the lower part of the range of\r\n" );
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document.write( "y = 2 + 2sec(2x) is 2 + 2(-1) = 2 - 2 = 0\r\n" );
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document.write( "So the lower part of the range is (, 0].\r\n" );
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document.write( "Therefore the range is (, 0] U [4, )\r\n" );
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document.write( "Edwin

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