document.write( "Question 466479: Determine whether the graph of y = | x | + 3 is symmetric with respect to the origin, the x-axis, or the y-axis. \n" ); document.write( "
Algebra.Com's Answer #319800 by ccs2011(207)\"\" \"About 
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Graph of \"y+=+abs%28x%29+%2B+3\"
\n" ); document.write( "\"graph%28200%2C200%2C-4%2C4%2C-1%2C7%2Cabs%28x%29+%2B+3%29\"\r
\n" ); document.write( "\n" ); document.write( "To test for symmetry, imagine folding the graph along an axis
\n" ); document.write( "If the graph folds on top of each other it is symmetric
\n" ); document.write( "Thus it is symmetric about the y-axis\r
\n" ); document.write( "\n" ); document.write( "Another way to check is to use points:
\n" ); document.write( "If its symmetric about the y-axis then:
\n" ); document.write( "For all points (a,b) if point (a,b) is on graph then point(-a,b) will also be on graph
\n" ); document.write( "Let (a,b) be (2,5) --> y = |2| +3 = 5
\n" ); document.write( "Then evaluate (-2,5) --> y = |-2| +3 = 2+3 = 5
\n" ); document.write( "It works\r
\n" ); document.write( "\n" ); document.write( "If its symmetric about the x-axis then:
\n" ); document.write( "For all points (a,b)if point (a,b) is on graph then point(a,-b) will also be on graph
\n" ); document.write( "Let (a,b) be (2,5) --> y = |2| +3 = 5
\n" ); document.write( "Then evaluate (2,-5) --> y = |2| +3 = 5
\n" ); document.write( "It Does Not work\r
\n" ); document.write( "\n" ); document.write( "If its symmetric about the origin then:
\n" ); document.write( "For all points (a,b)if point (a,b) is on graph then point(-a,-b) will also be on graph
\n" ); document.write( "Let (a,b) be (2,5) --> y = |2| +3 = 5
\n" ); document.write( "Then evaluate (-2,-5) --> y = |-2| +3 = 2+3 = 5
\n" ); document.write( "It Does Not work
\n" ); document.write( "Therefore the function is only symmetric about y-axis \n" ); document.write( "
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