document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=157686>Question 157686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, can you please help, can you please help with this piecewise defined function<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Piecewise defined function<BR>\n" );
document.write( ".<BR>\n" );
document.write( "f(x) = { x - 4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C=+2+ ALIGN=MIDDLE  ALT=\"+x+%3C=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > }<BR>\n" );
document.write( ".........{ 2x + 3, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+%3C+x+%3C=+14+ ALIGN=MIDDLE  ALT=\"+2+%3C+x+%3C=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > }<BR>\n" );
document.write( ".........{ 36, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E+14+ ALIGN=MIDDLE  ALT=\"+x+%3E+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > }<BR>\n" );
document.write( ".<BR>\n" );
document.write( "I think the domain is ( <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=+%2B+infinity+ ALIGN=MIDDLE  ALT=\"+%2B+infinity+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
document.write( ".<BR>\n" );
document.write( "I think the range is ( <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=+-2+ ALIGN=MIDDLE  ALT=\"+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ] U ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7+ ALIGN=MIDDLE  ALT=\"+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+31+ ALIGN=MIDDLE  ALT=\"+31+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ] U { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+36+ ALIGN=MIDDLE  ALT=\"+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" > }<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Is this domain, and range right? Can you please confirm? Please use interval notation, just like what I used for the domain and range<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Thanks ahead of time, Levi  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116194 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=116194\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = { x - 4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C=+2+ ALIGN=MIDDLE  ALT=\"+x+%3C=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > }<BR>\n" );
document.write( ".........{ 2x + 3, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+%3C+x+%3C=+14+ ALIGN=MIDDLE  ALT=\"+2+%3C+x+%3C=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > }<BR>\n" );
document.write( ".........{ 36, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E+14+ ALIGN=MIDDLE  ALT=\"+x+%3E+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
document.write( "\n" );
document.write( "f is defined using three formulas for linear function, so graph all three of them\r<BR>\n" );
document.write( "\n" );
document.write( " graph first this linear function: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=++x+-+4 ALIGN=MIDDLE  ALT=\"f%28x%29+=++x+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C=+2+ ALIGN=MIDDLE  ALT=\"+x+%3C=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...........since we have a restriction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C=+2+ ALIGN=MIDDLE  ALT=\"+x+%3C=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, erase the part <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=2 ALIGN=MIDDLE  ALT=\"x%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the domain is ( <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=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "then graph this linear function: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=++2x+%2B+3 ALIGN=MIDDLE  ALT=\"f%28x%29+=++2x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+%3C+x+%3C=+14+ ALIGN=MIDDLE  ALT=\"+2+%3C+x+%3C=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...........since we have a restriction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%3C=x+ ALIGN=MIDDLE  ALT=\"+2%3C=x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, erase the part from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the part where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+14 ALIGN=MIDDLE  ALT=\"x+%3E=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this graph will be a line segment from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=14 ALIGN=MIDDLE  ALT=\"x=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the domain is ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14+ ALIGN=MIDDLE  ALT=\"+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "then graph this linear function: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+36 ALIGN=MIDDLE  ALT=\"f%28x%29+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E+14+ ALIGN=MIDDLE  ALT=\"+x+%3E+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is constant function, so it is define for [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14+%3C+x+%3Cinfinity ALIGN=MIDDLE  ALT=\"+14+%3C+x+%3Cinfinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "the domain is [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14+%3C+x+%3Cinfinity ALIGN=MIDDLE  ALT=\"+14+%3C+x+%3Cinfinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );