document.write( "Question 1203313: Decide whether the relation defines y as a function of x. Give the domain and range.
\n" ); document.write( " x+y<3 \n" ); document.write( "
Algebra.Com's Answer #838762 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "The relation x+y < 3 is not a function because an input like x = 2 corresponds to infinitely many y outputs.
\n" ); document.write( "x+y < 3
\n" ); document.write( "2+y < 3
\n" ); document.write( "y < 3-2
\n" ); document.write( "y < 1
\n" ); document.write( "Simply select any value smaller than 1
\n" ); document.write( "Therefore points like (2,0), (2,-1), (2, -2), etc are all solutions.
\n" ); document.write( "They form a vertical column.
\n" ); document.write( "As such, this example is a visual indication we have failed the vertical line test.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If on the other hand the relation is x+y = 3, then this would be a function. Each x input corresponds to one and exactly one y output. The graph of x+y = 3, aka y = -x+3, passes the vertical line test.
\n" ); document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C-100%2C-x%2B3%29\"
\n" ); document.write( "This diagonal line passes through (0,3) and (3,0). These points represent the y-intercept and x-intercept respectively.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The green graph passes the vertical line test. This is because it is impossible to draw a single vertical line through more than one point on the green line.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "With regard to the function y = -x+3, we have:
\n" ); document.write( "Domain = set of all real numbers
\n" ); document.write( "Range = set of all real numbers
\n" ); document.write( " \n" ); document.write( "
\n" );