document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=96911>Question 96911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help, my teacher just gives us the lessons to do as homework and does not explain anything.<BR>\n" );
document.write( "Algebra 1, page 47, #14.<BR>\n" );
document.write( "a. Write a rule for the function -- Input - 0, 1, 2, 3 and Output - 0, .5, 2, 4.5\r<BR>\n" );
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document.write( "b. Find the value of y so that (1.5,y) is on the graph of the function.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #70529 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=70529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
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document.write( "Start with the given relation:<BR>\n" );
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document.write( "<th>Input</th><th>Output</th>\r\n" );
document.write( "<tr><TD >0</TD><TD >0</TD></tr>\r\n" );
document.write( "<tr><TD >1</TD><TD >0.5</TD></tr>\r\n" );
document.write( "<tr><TD >2</TD><TD >2</TD></tr>\r\n" );
document.write( "<tr><TD >3</TD><TD >4.5</TD></tr>\r\n" );
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document.write( "Rewrite 0.5 as 1/2 and 4.5 as 9/2<BR>\n" );
document.write( "<TABLE  cellspacing=15>\n" );
document.write( "<th>Input</th><th>Output</th>\r\n" );
document.write( "<tr><TD >0</TD><TD >0</TD></tr>\r\n" );
document.write( "<tr><TD >1</TD><TD >1/2</TD></tr>\r\n" );
document.write( "<tr><TD >2</TD><TD >2</TD></tr>\r\n" );
document.write( "<tr><TD >3</TD><TD >9/2</TD></tr>\r\n" );
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document.write( "Notice 0 can be written as 0/2 and 2 as 4/2<BR>\n" );
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document.write( "<th>Input</th><th>Output</th>\r\n" );
document.write( "<tr><TD >0</TD><TD >0/2</TD></tr>\r\n" );
document.write( "<tr><TD >1</TD><TD >1/2</TD></tr>\r\n" );
document.write( "<tr><TD >2</TD><TD >4/2</TD></tr>\r\n" );
document.write( "<tr><TD >3</TD><TD >9/2</TD></tr>\r\n" );
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document.write( "</TABLE>\r<BR>\n" );
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document.write( "So we can see that new output sequence is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F2 ALIGN=MIDDLE  ALT=\"0%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F2 ALIGN=MIDDLE  ALT=\"4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2 ALIGN=MIDDLE  ALT=\"9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice how the numerators follow the sequence \r<BR>\n" );
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document.write( "0,1,4,9\r<BR>\n" );
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document.write( "which is the sequence of perfect squares. So the numerator can be described with the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So that means we get the function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "---------------------------------------------------------------------------------------\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "To find f(x) when x=1.5 (or 3/2) plug in that value of x to find f(x)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%283%2F2%29%5E2%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29=%283%2F2%29%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%289%2F4%29%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29=%289%2F4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Square the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%289%2F4%29%2A%281%2F2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%289%2F4%29%2A%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the second fraction and multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=9%2F8 ALIGN=MIDDLE  ALT=\"f%28x%29=9%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=9%2F8 ALIGN=MIDDLE  ALT=\"f%28x%29=9%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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