document.write( "Question 1100839: For what value(s) of k will the relation not be a function? B = {(0.5k-5, 10), (k+7, 4)} \n" ); document.write( "
Algebra.Com's Answer #715384 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "The relation will NOT be a function if the inputs are equal. Repeated inputs leading to different outputs mean we won't have a function. In other words, a function is only possible if for any given input, there is exactly one output\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Set the inputs 0.5k-5 and k+7 equal to each other. Then solve for k\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "0.5k-5 = k+7
\n" ); document.write( "0.5k-5-0.5k = k+7-0.5k
\n" ); document.write( "-5 = 0.5k+7
\n" ); document.write( "-5-7 = 0.5k+7-7
\n" ); document.write( "-12 = 0.5k
\n" ); document.write( "0.5k = -12
\n" ); document.write( "0.5k/0.5 = -12/0.5
\n" ); document.write( "k = -24\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if k = -24, then the expressions 0.5k-5 and k+7 will be equal to each other. What will they be equal to? Let's find out
\n" ); document.write( "k+7 = -24+7 = -17
\n" ); document.write( "0.5*k-5 = 0.5*(-24)-5 = -12-5 = -17
\n" ); document.write( "Both inputs will be equal to -17 if k = -24\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The relation B = {(0.5k-5, 10), (k+7, 4)} will update to B = {(-17, 10), (-17, 4)} when k = -24. This relation is NOT a function due to the fact the input x = -17 leads to more than one output (y = 10 and y = 4 at the same time).
\n" ); document.write( " \n" ); document.write( "
\n" );