document.write( "Question 169368: I have come to a point in solving : is this function one-to-one, where the absolute value of a = the absolute value of b. Can this be one to one?\r
\n" ); document.write( "\n" ); document.write( "For the record, the problem states: f(x)= |x| - 2\r
\n" ); document.write( "\n" ); document.write( "I assigned a and b, and equal them to each other.\r
\n" ); document.write( "\n" ); document.write( "|a| - 2 = |b| - 2 ; add two to both sides\r
\n" ); document.write( "\n" ); document.write( "|a| = |b|\r
\n" ); document.write( "\n" ); document.write( "therefore a = b? or not really? Thank you for your help!! \n" ); document.write( "

Algebra.Com's Answer #124871 by Edwin McCravy(20060) $\"\"$ $\"About$

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: I have come to a point in solving : is this function one-to-one, where the absolute value of a = the absolute value of b. Can this be one to one?
\n" ); document.write( "For the record, the problem states: f(x)= |x| - 2
\n" ); document.write( "I assigned a and b, and equal them to each other.
\n" ); document.write( "|a| - 2 = |b| - 2 ; add two to both sides
\n" ); document.write( "|a| = |b|
\n" ); document.write( "therefore a = b? or not really?
\n" ); document.write( "

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document.write( "No it does not! for instance we could take a=3 and b=-3, then\r\n" );
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document.write( "|3| = |-3|\r\n" );
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document.write( "Another way to say it is it's not one-to-one because,\r\n" );
document.write( "for instance f(3) = f(-3) =  1 but 3 does not equal -3.   \r\n" );
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document.write( "The points (3,1) and (-3,1) are both on the graph and\r\n" );
document.write( "a horizontal line goes through them both, so the graph does not pass the horizontal line test.\r\n" );
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document.write( "The graph looks like this:\r\n" );
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document.write( "And as you see, the horizontal lines cut it more than\r\n" );
document.write( "once, so it cannot be one-to-one.\r\n" );
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document.write( "Edwin

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