document.write( "Question 238636: Can you explain why y=x^2 is the graph of a function of x, while x=y^2 is not the graph of a function of x? \n" ); document.write( "

Algebra.Com's Answer #175355 by josmiceli(19441) $\"\"$ $\"About$

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In order to be a function, each $\"x\"$ must match with a single
\n" ); document.write( " $\"f%28x%29\"$ . In the 1st case, $\"f%28x%29+=+x%5E2\"$ , and there can only be
\n" ); document.write( "one $\"x\"$ for each $\"f%28x%29\"$ .
\n" ); document.write( "In the 2nd case, $\"+f%28x%29+=+%2B+sqrt%28x%29\"$ , and $\"f%28x%29+=+-sqrt%28x%29\"$
\n" ); document.write( "Each $\"x\"$ matches with 2 values of $\"f%28x%29\"$
\n" ); document.write( "Here's a graph of each. The curve on the right is not a function
\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2C+sqrt%28x%29%2C+-sqrt%28x%29%29+\"$ \n" ); document.write( "

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