document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198334>Question 1198334</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State the domain and range. Explain how you find these mathematically without the use of a graph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(4) y = 25(-7x-4)64\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "(5) y = x2 / (x2-16)\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "(6) Let “M” be the set of motor vehicle owners who are registered in Ohio. Let “R” be the set of all motor vehicle registration numbers. Is the correspondence between M and R a function? Why, or why not? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831908 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=831908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "State the domain and range. Explain how you find these mathematically without the use of a graph.\r<BR>\n" );
document.write( "\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+25%28-7x-4%29%5E64 ALIGN=MIDDLE  ALT=\"y+=+25%28-7x-4%29%5E64\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........assuming you have that\r<BR>\n" );
document.write( "\n" );
document.write( "domain \r<BR>\n" );
document.write( "\n" );
document.write( "as you can  see, no matter what <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is, function is defined \r<BR>\n" );
document.write( "\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "range\r<BR>\n" );
document.write( "\n" );
document.write( "extreme points\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25%28-7x-4%29%5E64+=0 ALIGN=MIDDLE  ALT=\"+25%28-7x-4%29%5E64+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-7x-4%29%5E64+=0 ALIGN=MIDDLE  ALT=\"+%28-7x-4%29%5E64+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-7x-4+=0 ALIGN=MIDDLE  ALT=\"+-7x-4+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-7x+=4 ALIGN=MIDDLE  ALT=\"+-7x+=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=-4%2F7 ALIGN=MIDDLE  ALT=\"+x+=-4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........minimum  is  at  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F7 ALIGN=MIDDLE  ALT=\"-4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "so,  the  range  for  interval  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  is\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E+=0 ALIGN=MIDDLE  ALT=\"y%3E+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(5) \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+%2F+%28x%5E2-16%29 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+%2F+%28x%5E2-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "domain \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+%2F+%28%28x-4%29%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+%2F+%28%28x-4%29%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >->zeros <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "denominator cannot be zero\r<BR>\n" );
document.write( "\n" );
document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E4 ALIGN=MIDDLE  ALT=\"x%3C%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-4 ALIGN=MIDDLE  ALT=\"x%3C%3E-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and domain  is\r<BR>\n" );
document.write( "\n" );
document.write( "{ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-4 ALIGN=MIDDLE  ALT=\"x%3C%3E-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E4 ALIGN=MIDDLE  ALT=\"x%3C%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "range<BR>\n" );
document.write( "The range is the set of y for which the discriminant is greater or equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+%2F+%28x%5E2-16%29 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+%2F+%28x%5E2-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28x%5E2-16%29+=+x%5E2++ ALIGN=MIDDLE  ALT=\"y%28x%5E2-16%29+=+x%5E2++\"   DISABLED_style= \"max-width:90%; height:auto;\" >->discriminant is\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64y%5E2-64y%3E=0 ALIGN=MIDDLE  ALT=\"64y%5E2-64y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64y%28y-1%29%3E=0 ALIGN=MIDDLE  ALT=\"64y%28y-1%29%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=0 ALIGN=MIDDLE  ALT=\"y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=1 ALIGN=MIDDLE  ALT=\"y%3E=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The range is \r<BR>\n" );
document.write( "\n" );
document.write( "{  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+ ALIGN=MIDDLE  ALT=\"R+\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=0 ALIGN=MIDDLE  ALT=\"y%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E1 ALIGN=MIDDLE  ALT=\"y%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  }\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(6) Let “M” be the set of motor vehicle owners who are registered in Ohio. Let “R” be the set of all motor vehicle registration numbers. Is the correspondence between M and R a function? Why, or why not?\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=No ALIGN=MIDDLE  ALT=\"No\"   DISABLED_style= \"max-width:90%; height:auto;\" > because for a correspondence to be a function there must be a one-to-one correspondence.<BR>\n" );
document.write( "For each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > value, there must be a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=unique ALIGN=MIDDLE  ALT=\"unique\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y ALIGN=MIDDLE  ALT=\"+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > value.<BR>\n" );
document.write( "For cars, this means that each owner can only register one car in his or her name.<BR>\n" );
document.write( "As you know, some people have only one car but many people have multiple cars in their name.<BR>\n" );
document.write( "So there is not a one-to-one correspondence, so it can't be a function.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );