document.write( "Question 1203502: What is the range of the function given by the following graph, and how did you figure it out?
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Algebra.Com's Answer #839118 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"graph%28400%2C200%2C-12%2C12%2C-6%2C6%2C48%2F%28%28x-4%29%28x%2B4%29%29%29\"\r\n" );
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document.write( "It have vertical asymptotes x=4 and x=-4, so the denominator\r\n" );
document.write( "must contain (x-4)(x+4).\r\n" );
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document.write( "It has the x-axis as a horizontal asymptote, so the numerator\r\n" );
document.write( "must be of lower degree than the denominator. so it has the\r\n" );
document.write( "form: \r\n" );
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document.write( "\"f%28x%29\"\"%22%22=%22%22\"\"%28ax%2Bb%29%2F%28%28x-4%29%28x%2B4%29%29\"\r\n" );
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document.write( "It passes through (0,-3), so f(0) = -3\r\n" );
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document.write( "\"-3\"\"%22%22=%22%22\"\"%28a%280%29%2Bb%29%2F%28%280-4%29%280%2B4%29%29\"\r\n" );
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document.write( "\"-3\"\"%22%22=%22%22\"\"%28b%29%2F%28-16%29%29\"\r\n" );
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document.write( "\"48=b\"\r\n" );
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document.write( "It is symmetrical with respect to the y axis, \r\n" );
document.write( "therefore f(x) = f(-x)\r\n" );
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document.write( "\"f%28-x%29\"\"%22%22=%22%22\"\"%28a%28-x%29%2B48%29%2F%28%28-x-4%29%28-x%2B48%29%29\"\r\n" );
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document.write( "So\r\n" );
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document.write( "\"%28ax-48%29%2F%28%28x-4%29%28x%2B4%29%29\"\"%22%22=%22%22\"\"%28a%28-x%29%2Bb%29%2F%28%28-x-4%29%28-x%2B4%29%29\"\r\n" );
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document.write( "\"ax%2B48\"\"%22%22=%22%22\"\"a%28-x%29%2B48\"\r\n" );
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document.write( "\"ax=-ax\"\r\n" );
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document.write( "a = -a for all values of x, thus a=0\r\n" );
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document.write( "The equation is\r\n" );
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document.write( "\"f%28x%29\"\"%22%22=%22%22\"\"48%2F%28%28x-4%29%28x%2B4%29%29\"\r\n" );
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document.write( "The range is (-infinity,-3] U (0,infinity)\r\n" );
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document.write( "Edwin
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