document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=950516>Question 950516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't know if I understand what f(x) =.... means\r<BR>\n" );
document.write( "\n" );
document.write( "does the f mean function of \"x\" and whatever value we plug in for x results in our y value. Therefore, y can only be found relative to the x value chosen? Assuming this is correct why isn't it the other way around why can't we compute what x is relative to y like: f(y)=x? why isn't it done this way? I don't think I understand what functions are or exactly what f(x) is actually saying.\r<BR>\n" );
document.write( "\n" );
document.write( "Please help me understand thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #580443 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=580443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A function is this thing that will take an input and chew it up and, based on what the input is, will give you a given output. Think of a sausage maker. You put the meat and herbs and spices on one end and it grinds the meat and produce a sausage at the other end.<BR>\n" );
document.write( "So,a function is a special relationship where each input has a single output. \r<BR>\n" );
document.write( "\n" );
document.write( "It is often written just the way you have it, \"f(x)\" where x is the input value. But it's not limited to x. You could have S(n) or any other symbol.\r<BR>\n" );
document.write( "\n" );
document.write( "Example: f(x) = x/2 (\"f of x is x divided by 2\") is a function, because each input \"x\" has a single output \"x/2\". We can substitute x with values:<BR>\n" );
document.write( "• f(2) = 1<BR>\n" );
document.write( "• f(16) = 8<BR>\n" );
document.write( "• f(&#8722;10) = &#8722;5<BR>\n" );
document.write( "Example: f(x) = x^2<BR>\n" );
document.write( "• f(2) = 4<BR>\n" );
document.write( "• f(5) = 25\r<BR>\n" );
document.write( "\n" );
document.write( "But a function has special rules:\r<BR>\n" );
document.write( "\n" );
document.write( "    - It must work for every possible input value<BR>\n" );
document.write( "    - And it has only one relationship for each input value\r<BR>\n" );
document.write( "\n" );
document.write( "A more formal definition is: A function relates each element of a set<BR>\n" );
document.write( "with exactly one element of another set, which can possibly the same set.<BR>\n" );
document.write( "Each element means that every element in X is related to some element in Y. We say that the function covers X, which means that it relates every element of x. Note: That only applies to the elements of x. Some elements of Y might not be related to at all, and that's fine.<BR>\n" );
document.write( "\"...exactly one element of another set...\" means that a function is single valued. It will not give back 2 or more results for the same input.\r<BR>\n" );
document.write( "\n" );
document.write( "Now think back to the sausage maker. It takes all the ingredients and produces one sausage. Likewise with functions, many-to-one is allowed but one-to-many is not.<BR>\n" );
document.write( "Well, I've run out of time. I hope I've helped in some small way. Don't give up part of the difficulty with math is, it's like learning a foreign language. Once you learn the vocabulary, the rest is like putting together a jigsaw puzzle, it's very mechanical. Have faith in yourself, if you don't, who will? Best of luck\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );