document.write( "Question 694712: Is this a function: {(x.y) | x^2 +(y-1)^2 = 4} \n" ); document.write( "

Algebra.Com's Answer #428183 by MathLover1(20850) $\"\"$ $\"About$

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{(x.y) | $\"x%5E2+%2B%28y-1%29%5E2+=+4\"$ }
\n" ); document.write( "What is a $\"Function\"$ ?\r
\n" ); document.write( "\n" ); document.write( "A $\"function\"$ relates $\"an\"$ $\"+input\"$ to $\"an\"$ $\"+output\"$ .\r
\n" ); document.write( "\n" ); document.write( "A $\"function\"$ is a $\"rule\"$ that assigns $\"uniquely\"$ to a member of $\"domain\"$ $\"+set\"$ , a member of the $\"range\"$ set. The key word is \" $\"uniquely\"$ \". \r
\n" ); document.write( "\n" ); document.write( "So if you assign say $\"x=2\"$ as well as $\"x=-2\"$ to number $\"y=1\"$ , then you $\"have\"$ a $\"rule\"$ , but $\"not\"$ a $\"function\"$ . That is the logic behind the $\"vertical\"$ $\"+line\"$ $\"+test\"$ . If you draw a vertical line and it intersects the graph of the function in $\"two\"$ $\"+distinct\"$ $\"+points\"$ , then you can see that it means you have assigned both of these points to the point where your vertical line $\"crosses\"$ the $\"x-axis\"$ . \r
\n" ); document.write( "\n" ); document.write( "An example of this is the $\"circle\"$ , and you have a $\"circle\"$ .\r
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