document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183634>Question 1183634</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a) For the following relations from the set A = {a, b, c} and the set B = {x, y, z} does the relation satisfy the definition of a function? If yes, state why it is a function and also give the domain, co-domain, and range. If not state which of the function definition conditions are violated. For each relation, you will be required to draw an arrow diagram\r<BR>\n" );
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document.write( "(i) The relation that is represented by the ordered pairs (a, x), (b, y).\r<BR>\n" );
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document.write( "(ii)The relation that is represented by the ordered pairs (a, y), (b, y), (c, z).\r<BR>\n" );
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document.write( "(iii)The relation that is represented by the ordered pairs (a, x), (b, y), (c, z), (a, z).\r<BR>\n" );
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document.write( "(b) We now introduce a third set C = {r, s, t)Let the functions f: A right arrow B be defined by the ordered pairs (a, y), (b, x), (c, y), and g: B right arrow C be defined by the ordered pairs (x, s), (y, t), (z, r).\r<BR>\n" );
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document.write( "(i) Compute the elements corresponding to the composite function g composite function f: A right arrow C and represent them in an arrow diagram (this will require more than one mapping in the diagram)\r<BR>\n" );
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document.write( "(ii)Find the ranges of f, g, and g composite function f. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814052 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814052\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "(a) (i): Function because each element of the domain set maps to only one element of the range set. Domain = {a, b, c}. Codomain = {x, y, z}.  Range = {x, y}\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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