document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102716>Question 1102716</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 2014, the cost of a first class postage stamp was $0.49. Weight is in ounces and cost is in dollars. The ordered pairs listed are (1,0.49),(2,0.70),(3,0.91), and (3.5, 1.12). Write a function to represent the cost of mailing a stamped letter that weighs between 0 and 3.5 ounces. What type of function is it?  </SPAN>\n" );
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document.write( "Your statement of the problem doesn't make it clear; but in fact this function is a step function.  The given data points tell us<BR>\n" );
document.write( "1 ounce --> 49 cents<BR>\n" );
document.write( "2 ounces --> 70 cents<BR>\n" );
document.write( "3 ounces --> 91 cents<BR>\n" );
document.write( "3.5 ounces --> $1.12<br><BR>\n" );
document.write( "The first three data points make this look like a linear function -- specifically, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+28%2B.21x ALIGN=MIDDLE  ALT=\"C+=+28%2B.21x\"   DISABLED_style= \"max-width:90%; height:auto;\" > where x is the weight in ounces of the letter.  However, the cost of mailing a letter weighing (for example) 2.35 ounces is 91 cents, not 28+2.35(21)=77.35 cents.<br><BR>\n" );
document.write( "The step function (a piecewise function) giving the cost of postage for mailing a letter weighing between 0 and 3.5 ounces is<BR>\n" );
document.write( "C = .49, if 0<=x<1;<BR>\n" );
document.write( "C = .70, if 1<=x<2;<BR>\n" );
document.write( "C = .91, if 2<=x<3;<BR>\n" );
document.write( "C = 1.21, if 3<=x<=3.5<br><BR>\n" );
document.write( "You could write this function without using a piecewise function by using the floor function, where floor(x) is the largest integer less than or equal to x:<BR>\n" );
document.write( "C = .49 + .21*floor(x)<BR>\n" );
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