document.write( "Question 1142368: Please help me solve this:\r
\n" ); document.write( "\n" ); document.write( "Which of the following relations is a function / are functions?\r
\n" ); document.write( "\n" ); document.write( "A. {(a, b), (a, c), (a, d), (a, e)}
\n" ); document.write( "B. {(b, a), (c, a), (d, a), (e, a)}
\n" ); document.write( "C. {(1, 1), (2, sqrt(2)), (3, sqrt(3)), (4, 2)}
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\n" ); document.write( "1. Only A
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\n" ); document.write( "3. Only C
\n" ); document.write( "4. Only B and C
\n" ); document.write( "5. A, B \n" ); document.write( "

Algebra.Com's Answer #763116 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "When you see this:
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document.write( "A. {(a, b), (a, c), (a, d), (a, e)}\r
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document.write( "Think  \"x=a, y=b\",  \"x=a, y=c\", \"x=a, y=d\", \"x=a, y=e\".\r
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document.write( "A function must have one value of y for each value of x, otherwise it does not meet the definition of 'function.'    In this example, do you see exactly one value of y for a given value of x?   No, because for x=a, y has 4 different values  (just having two different y values would be enough to disqualify it as a function).\r
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document.write( "Looking at case B, what do you think?  A function?   We see multiple occurrences of y=a, but each at different values of x.   This is OK for a function.  For example, look at the graph of a 4th order polynomial :\r
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document.write( "There are multiple places where y is the same value but that happens for different values of x.  If one dragged a vertical line along the x-axis, you would see it only intersects the graph once for each value of x that you pick. This is a function.\r
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document.write( "I will leave C to you.  Just remember  is by definition the principal square root of x  (i.e. the nonnegative square root only).    \r
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