document.write( "Question 360500:
\n" ); document.write( "If \"%22f%28x%29%22=+sqrt%289-x%5E2%29\", how many integers are in the domain of f ?\r
\n" ); document.write( "\n" ); document.write( "a none
\n" ); document.write( "b 3
\n" ); document.write( "c 4
\n" ); document.write( "d 7
\n" ); document.write( "e infinely many \n" ); document.write( "
Algebra.Com's Answer #257216 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\"%22f%28x%29%22=+sqrt%289-x%5E2%29\"
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document.write( "We require that the expression under the radical, the \"radicand\",\r\n" );
document.write( "is not negative, but is 0 or something greater. \r\n" );
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document.write( "\"9-x%5E2%3E=0\"\r\n" );
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document.write( "\"%283-x%29%283%2Bx%29%3E=0\"\r\n" );
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document.write( "The expression on the left has zeros 3 and -3, so we\r\n" );
document.write( "mark these solid on a number line:\r\n" );
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document.write( "-------------@-----------------------@--------\r\n" );
document.write( "-6  -5  -4  -3  -2  -1   0   1   2   3   4   5  \r\n" );
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document.write( "We choose a test value on the left of -3, say -4, and\r\n" );
document.write( "substitute it in:\r\n" );
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document.write( "\"%283-x%29%283%2Bx%29%3E=0\"\r\n" );
document.write( "\"%283-%28-4%29%29%283%2B%28-4%29%29%3E=0\"\r\n" );
document.write( "\"%283%2B4%29%283-4%29%3E=0\"\r\n" );
document.write( "\"%287%29%28-1%29%3E=0\"\r\n" );
document.write( "\"-7%3E=0\"\r\n" );
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document.write( "This is false so we do not shade to the left of -3\r\n" );
document.write( "So we still have:\r\n" );
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document.write( "-------------@-----------------------@--------\r\n" );
document.write( "-6  -5  -4  -3  -2  -1   0   1   2   3   4   5\r\n" );
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document.write( "We choose a test value between -3 and +3, say 0, and\r\n" );
document.write( "substitute it in:\r\n" );
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document.write( "\"%283-x%29%283%2Bx%29%3E=0\"\r\n" );
document.write( "\"%283-%280%29%29%283%2B%280%29%29%3E=0\"\r\n" );
document.write( "\"%283-0%29%283%2B0%29%3E=0\"\r\n" );
document.write( "\"%283%29%283%29%3E=0\"\r\n" );
document.write( "\"9%3E=0\"\r\n" );
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document.write( "This is true so we shade the part of the number line between\r\n" );
document.write( "-3 and +3 inclusive of -3 and 3 since the inequality is \"%22%22%3E=%22%22\"\r\n" );
document.write( "and not >.  So we have:\r\n" );
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document.write( "-------------@=======================@--------\r\n" );
document.write( "-6  -5  -4  -3  -2  -1   0   1   2   3   4   5\r\n" );
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document.write( "We choose a test value on the right of +3, say +4, and\r\n" );
document.write( "substitute it in:\r\n" );
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document.write( "\"%283-x%29%283%2Bx%29%3E=0\"\r\n" );
document.write( "\"%283-%284%29%29%283%2B%284%29%29%3E=0\"\r\n" );
document.write( "\"%283-4%29%283%2B4%29%3E=0\"\r\n" );
document.write( "\"%28-1%29%287%29%3E=0\"\r\n" );
document.write( "\"-7%3E=0\"\r\n" );
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document.write( "This is false so we do not shade to the right of 3\r\n" );
document.write( "So we still have:\r\n" );
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document.write( "-------------@=======================@--------\r\n" );
document.write( "-6  -5  -4  -3  -2  -1   0   1   2   3   4   5\r\n" );
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document.write( "and the domain is [-3,3]\r\n" );
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document.write( "The integers in the domain are -3, -2, -1, 0, 1, 2, 3.\r\n" );
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document.write( "So the answer is 7, choice d.\r\n" );
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document.write( "Edwin
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