document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87929>Question 87929</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain the meaning of a function. Give an example </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63807 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=63807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The official definition of a function is any set of points such that no two distinct points have the same x coordinate.  I prefer to think in a more informal way.  First of all a relation is any set of points.  This is so named because there is a \"relationship\" between the variables.  With a relation, if you have a particular x value, there could be two or more y values associated with that x value.  However, a function is a special set of points that has a uniqueness property--each x value has ONLY one y value.  As examples, the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a function, because each x value has ONLY one y value.  However, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2 ALIGN=MIDDLE  ALT=\"x=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a function, because, if you choose a value of x, like x= 4, there are TWO values of y (y= 2 or y=-2) that would give you x = 4. \r<BR>\n" );
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document.write( "Also, see my website for a page in MATH IN LIVING COLOR.  Click on my tutor name \"rapaljer\" anywhere in algebra.com. After you find my Math in Living Color page, go to \"College Algebra\", and look for \"Section 2.07 Functions, Domain, and Range.\"  I hope that will be helpful to you and anyone else who needs help with Functions, Domain, and Range.\r<BR>\n" );
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document.write( "R^2  Retired from SCC   </SPAN>\n" );
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