document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085943>Question 1085943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please may you help me immediately to solve this problem: a.suppose the international airmail on articles/packets to countries in zone 1 are given below.<BR>\n" );
document.write( "Weight (w)  cost in kina<BR>\n" );
document.write( "Up to 50        55<BR>\n" );
document.write( "Up to 150       110<BR>\n" );
document.write( "Up to 250       180<BR>\n" );
document.write( "Up to 1kg       290<BR>\n" );
document.write( "Up to 2kg       450\r<BR>\n" );
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document.write( "i.write the cost function,in function notation for the above.<BR>\n" );
document.write( "ii.Draw the graph of this function<BR>\n" );
document.write( "iii.state the domain and range of this function<BR>\n" );
document.write( "iv.does the graph really represent a function? Justify you answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700043 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">Part i)\r<BR>\n" );
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document.write( "The cost function is the piecewise function given below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/QJcS5VQ.png\">\r<BR>\n" );
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document.write( "where w is the weight in grams, and c(w) is the cost\r<BR>\n" );
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document.write( "The piecwise function basically says\r<BR>\n" );
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document.write( "c(w) = 55 if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+w+%3C=+50 ALIGN=MIDDLE  ALT=\"0+%3C=+w+%3C=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OR<BR>\n" );
document.write( "c(w) = 110 if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50+%3C+w+%3C=+150 ALIGN=MIDDLE  ALT=\"50+%3C+w+%3C=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OR<BR>\n" );
document.write( "c(w) = 180 if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150+%3C+w+%3C=+250 ALIGN=MIDDLE  ALT=\"150+%3C+w+%3C=+250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OR<BR>\n" );
document.write( "c(w) = 290 if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250+%3C+w+%3C=+1000 ALIGN=MIDDLE  ALT=\"250+%3C+w+%3C=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OR<BR>\n" );
document.write( "c(w) = 450 if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000+%3C+w+%3C=+2000 ALIGN=MIDDLE  ALT=\"1000+%3C+w+%3C=+2000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so we have 5 separate functions depending on what w is. The notation given previously (with the big single curly brace) is a more compact way to write the piecewise function.\r<BR>\n" );
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document.write( "Part ii)\r<BR>\n" );
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document.write( "The graph is shown <a  rel=nofollow HREF=\"https://i.imgur.com/kf35urK.png\">here</a>. The graph was created with GeoGebra (free graphing software).\r<BR>\n" );
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document.write( "Note how points {C, E, G, I} are open circles to indicate we do NOT include them as part of the function\r<BR>\n" );
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document.write( "The graph represents a <a  rel=nofollow HREF=\"http://www.mathwords.com/s/step_function.htm\">step function</a>\r<BR>\n" );
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document.write( "Part iii)\r<BR>\n" );
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document.write( "Domain: set of real numbers w such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+w+%3C=+2000 ALIGN=MIDDLE  ALT=\"0+%3C=+w+%3C=+2000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "basically saying that the weights can be as small as 0 grams or as large as 2000 grams (2 kg).\r<BR>\n" );
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document.write( "Range: c(w) can be only values drawn from this set: {55, 110, 180, 290, 450} \r<BR>\n" );
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document.write( "Those values are the given costs for each piece of the piecewise function (see part i)\r<BR>\n" );
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document.write( "Part iv)\r<BR>\n" );
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document.write( "Yes it's a function because it passes the <a  rel=nofollow HREF=\"http://www.mathwords.com/v/vertical_line_test.htm\">vertical line test</a>. \r<BR>\n" );
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document.write( "For any given input, there is EXACTLY ONE output. This adds further confirmation that we have a function here.</font> </SPAN>\n" );
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