document.write( "Question 1102474: the function “sgn b”, called the signum function, which is Latin for “sign”. For the purpose of this problem, we will define this function as follows:
\n" ); document.write( "sgnb={−1, b<0 } (the bracket should cover the whole thing)
\n" ); document.write( " { 1, b≥0 }
\n" ); document.write( "For example, sgn(17) = 1, sgn(−√2) = −1, and sgn(0) = 1.
\n" ); document.write( "d) If b is any real number, how does the expression |b| sgn b simplify? Explain briefly.
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Algebra.Com's Answer #717174 by KMST(5328) $\"\"$ $\"About$

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$\"sgn%28b%29\"$ $\"%22=%22\"$ $\"system%28%22-1+%2C+b%3C0%22%2C%221+%2C+b%3E=0%22%29\"$
\n" ); document.write( "If $\"b\"$ = any real number,
\n" ); document.write( " $\"abs%28b%29sgn%28b%29\"$ $\"%22=%22\"$

$\"%22=+b%22\"$ , so $\"highlight%28abs%28b%29sgn%28b%29=b%29\"$ .
\n" ); document.write( "For non-negative numbers, $\"b%3E=0\"$ ,
\n" ); document.write( "the signum function returns 1,
\n" ); document.write( "the absolute value function returns the original number,
\n" ); document.write( "and the product of the returned values is the original number.
\n" ); document.write( "For negative numbers,
\n" ); document.write( "the signum function returns $\"-1\"$ ,
\n" ); document.write( "the absolute value function returns the positive opposite of the original number,
\n" ); document.write( "and the product of the returned values is the original number.
\n" ); document.write( "In other words, for negative numbers,
\n" ); document.write( "the absolute value takes away the minus sign,
\n" ); document.write( "but the signum function then reapplies the minus sign that the absolute value function took away. \n" ); document.write( "

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