document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=36785>Question 36785</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please explain functions, relations and arguments.  I need guidance to answer the following questions:\r<BR>\n" );
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document.write( "1. Which of the following are functions?  Explain reasoning for a, b, and c.\r<BR>\n" );
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document.write( "a. 	f(x) = 2 if x>1<BR>\n" );
document.write( "  	f(x) = -1 otherwise\r<BR>\n" );
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document.write( "b.	f(x) = 5 if x>0<BR>\n" );
document.write( "	f(x) = -5 if x<0\r<BR>\n" );
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document.write( "c.	f(x) = 10/x\r<BR>\n" );
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document.write( "2. Suppose you have a lemonade stand, and when you charge $2 per cup of lemonad you sell 120 cups. But when you raise your price to $3 you only sell 60 cups.  Write an equation for the number of cups you sell as a function of the price you charge.  Denote \"C\" for number of cups, and \"P\" for the price you charge.  Assume the function is linear.\r<BR>\n" );
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document.write( "3.  Take a look at the table below and write out an equation for f(x).\r<BR>\n" );
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document.write( "x	-2	-1	0	1	2	   <BR>\n" );
document.write( "f(x)	-5	-2	1	4	7	 \r<BR>\n" );
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document.write( "4.  For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function.  Explain your reasoning thoroughly.\r<BR>\n" );
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document.write( "a. How fast it takes you to get to work as a function of how fast you drive.<BR>\n" );
document.write( "b. Probability of getting into a car accident as a function of how fast your drive.<BR>\n" );
document.write( "c. Your height as a function of age (from age 0 to 100).<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22590 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=22590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Which of the following are functions? Explain reasoning for a, b, and c. <BR>\n" );
document.write( "a. f(x) = 2 if x>1<BR>\n" );
document.write( "f(x) = -1 otherwise <BR>\n" );
document.write( "b. f(x) = 5 if x>0<BR>\n" );
document.write( "f(x) = -5 if x<0 <BR>\n" );
document.write( "c. f(x) = 10/x<BR>\n" );
document.write( "They are all functions, because \" for each value of \"x\" there is<BR>\n" );
document.write( "only one value of \"y\".<BR>\n" );
document.write( "Realations allow an x value to have several y value associates.<BR>\n" );
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document.write( "2. Suppose you have a lemonade stand, and when you charge $2 per cup of lemonad you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote \"C\" for number of cups, and \"P\" for the price you charge. Assume the function is linear.\r<BR>\n" );
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document.write( "You have two points to work with : (Price, # of cups)<BR>\n" );
document.write( "(2,120) and (3,60)<BR>\n" );
document.write( "The linear form is cups = (slope)(price)+ b<BR>\n" );
document.write( "slope = (120-60)/(2-3)=-60<BR>\n" );
document.write( "Then 120=-60(2)+b<BR>\n" );
document.write( "b=240<BR>\n" );
document.write( "Your equation is C=-60p+240  \r<BR>\n" );
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document.write( "3. Take a look at the table below and write out an equation for f(x). \r<BR>\n" );
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document.write( "x -2 -1 0 1 2 <BR>\n" );
document.write( "f(x) -5 -2 1 4 7 \r<BR>\n" );
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document.write( "Since there is a common difference of +3 in the y-values<BR>\n" );
document.write( "the relation is linear, i.e. y=mx+b<BR>\n" );
document.write( "Use two of the points to get the equation, as follows:<BR>\n" );
document.write( "Points: (0,1) (2,7)<BR>\n" );
document.write( "slope = (7-1)/2= 3<BR>\n" );
document.write( "1=3(0)+b<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "y=3x+1\r<BR>\n" );
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document.write( "4. For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function. Explain your reasoning thoroughly. <BR>\n" );
document.write( "a. How fast it takes you to get to work as a function of how fast you drive.\r<BR>\n" );
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document.write( "Linear: as average speed increases, time decreases<BR>\n" );
document.write( "b. Probability of getting into a car accident as a function of how fast your drive.<BR>\n" );
document.write( "Linear: as speed increases, probability of having an accident increases.<BR>\n" );
document.write( "c. Your height as a function of age (from age 0 to 100).\r<BR>\n" );
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document.write( "non-linear: age increases in a constant way; height does not.<BR>\n" );
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