document.write( "Question 1062378: 1. y² = x+1, 2. y² = 3-2x, and 3. x = |y| are not functions,
\n" ); document.write( "give reasons and what does the graph x = |y| look like? \n" ); document.write( "
Algebra.Com's Answer #677282 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
1. y² = x+1, 2. y² = 3-2x, and 3. x = |y| are not functions,
\n" ); document.write( "give reasons and what does the graph x = |y| look like?
\n" ); document.write( "
\r\n" );
document.write( "A function must not have two or more solutions in which the\r\n" );
document.write( "output (y-value) are different for the same input (x-value).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1. y² = x+1 is not a function because \r\n" );
document.write( "(x,y) = (3,2) and (x,y) = (3,-2) are both\r\n" );
document.write( "solutions, and there are two different\r\n" );
document.write( "outputs (y-values), 2 and -2, for the same\r\n" );
document.write( "input (x-value) of 3.\r\n" );
document.write( "\r\n" );
document.write( "To show that both (3,2) and (3,-2) are solutions:\r\n" );
document.write( "\r\n" );
document.write( "  y² = x+1        y² = x+1\r\n" );
document.write( "(2)² = 3+1     (-2)² = 3+1 \r\n" );
document.write( "   4 = 4           4 = 4\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2. y² = 3-2x\r\n" );
document.write( "\r\n" );
document.write( "is not a function because (x,y) = (-11,5) and \r\n" );
document.write( "(x,y) = (-11,-5) are both solutions, and there \r\n" );
document.write( "are two different outputs (y-values), 5 and -5, \r\n" );
document.write( "for the same input (x-value) of -11.\r\n" );
document.write( "\r\n" );
document.write( "To show that both (-11,5) and (-11,-5) are solutions:\r\n" );
document.write( "\r\n" );
document.write( "  y² = 3-2x           y² = 3-2x\r\n" );
document.write( "(5)² = 3-2(-11)    (-5)² = 3-2(-11) \r\n" );
document.write( "  25 = 3+22           25 = 3+22\r\n" );
document.write( "  25 = 25             25 = 25\r\n" );
document.write( "\r\n" );
document.write( "3. x = |y| is not a function because for \r\n" );
document.write( "example, (x,y) = (3,3) and (x,y) = (3,-3) \r\n" );
document.write( "are both solutions, and there are two \r\n" );
document.write( "different outputs (y-values), 3 and -3, \r\n" );
document.write( "for the same input (x-value) of 3.\r\n" );
document.write( "\r\n" );
document.write( "To show that both (3,3) and (3,-3) are solutions:\r\n" );
document.write( "\r\n" );
document.write( "   x = |y|         x = |y|\r\n" );
document.write( "   3 = |3|         3 = |-3| \r\n" );
document.write( "   3 = 3           3 = 3\r\n" );
document.write( "\r\n" );
document.write( "To get the graph of x = |y|\r\n" );
document.write( "\r\n" );
document.write( "Get some points  \r\n" );
document.write( "\r\n" );
document.write( "x | y\r\n" );
document.write( "0 | 0\r\n" );
document.write( "1 | 1\r\n" );
document.write( "1 |-1\r\n" );
document.write( "2 | 2\r\n" );
document.write( "2 |-2\r\n" );
document.write( "3 | 3\r\n" );
document.write( "3 |-3\r\n" );
document.write( "4 | 4\r\n" );
document.write( "4 |-4\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then draw the graph:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You can tell from the graph that it is not a function because \r\n" );
document.write( "it is possible to draw a vertical line through the graph and\r\n" );
document.write( "it will intersect the graph more than once, like the green vertical\r\n" );
document.write( "line below that intersects the graph twice:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );