document.write( "Question 585845: how to determine whether the equation defines y as a function of x. is it a function yes or no to the problem: x=y^2-6 and problem y=x^2+6 \n" ); document.write( "

Algebra.Com's Answer #373724 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+y=x%5E2%2B6\"$ defines y as a function of x, because for every x value there is no more than a y value. (In fact for every x there is exactly one y value). We can forgive a function if some values of x do not have a y, but if there is more than one y for even one value of x, then the relation is not a function.
\n" ); document.write( " $\"x=y%5E2-6\"$ does not define y as a function of x, because some value(s) of x have more than one y.
\n" ); document.write( "In general,
\n" ); document.write( " $\"x=y%5E2-6\"$ --> $\"x%2B6=y%5E2\"$ --> $\"y=sqrt%28x%2B6%29\"$ or $\"y=-sqrt%28x%2B6%29\"$
\n" ); document.write( "So, all the values of x larger than -6 would have two y values.
\n" ); document.write( "For example, x=10 would be paired with y=4 and y=-4.
\n" ); document.write( "A function cannot assign more than one y to any x value. \n" ); document.write( "

\n" );