document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152172>Question 1152172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain and range of the function: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+G%28t%29=1%2F%28t%5E2-16%29+ ALIGN=MIDDLE  ALT=\"+G%28t%29=1%2F%28t%5E2-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "For the domain, I set the denominator equal to 0 and added 16 to both sides. Then, I took the square root of both sides. This left me with t=4, therefore the domain would be all real numbers except 4. However, this was incorrect... how did I miss the -4 in the domain restriction?\r<BR>\n" );
document.write( "\n" );
document.write( "Also, how could I find the range?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774120 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=774120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+G%28t%29=1%2F%28t%5E2-16%29+ ALIGN=MIDDLE  ALT=\"+G%28t%29=1%2F%28t%5E2-16%29+\"   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=t%5E2-16+=0 ALIGN=MIDDLE  ALT=\"t%5E2-16+=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=t%5E2-4%5E2=0 ALIGN=MIDDLE  ALT=\"t%5E2-4%5E2=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=%28t-4%29%28t%2B4%29=0 ALIGN=MIDDLE  ALT=\"%28t-4%29%28t%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t-4%29=0 ALIGN=MIDDLE  ALT=\"%28t-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4 ALIGN=MIDDLE  ALT=\"t=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t%2B4%29=0 ALIGN=MIDDLE  ALT=\"%28t%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-4 ALIGN=MIDDLE  ALT=\"t=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<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=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > element of <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=t%3C%3E-4 ALIGN=MIDDLE  ALT=\"t%3C%3E-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%3C%3E-4+ ALIGN=MIDDLE  ALT=\"t%3C%3E-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "range:\r<BR>\n" );
document.write( "\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+G%28t%29=y ALIGN=MIDDLE  ALT=\"+G%28t%29=y\"   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=1%2F%28t%5E2-16%29+ ALIGN=MIDDLE  ALT=\"+y=1%2F%28t%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%28t%5E2-16%29+=1 ALIGN=MIDDLE  ALT=\"+y%28t%5E2-16%29+=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+yt%5E2-16y+=1 ALIGN=MIDDLE  ALT=\"+yt%5E2-16y+=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >......to both sides add -1 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+yt%5E2-16y+-1=0 ALIGN=MIDDLE  ALT=\"+yt%5E2-16y+-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> For a quadratic equation of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  the discriminant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=y ALIGN=MIDDLE  ALT=\"a=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-16y-1 ALIGN=MIDDLE  ALT=\"c=-16y-1\"   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=0%5E2-4y%28-16y-1%29%3E=0 ALIGN=MIDDLE  ALT=\"0%5E2-4y%28-16y-1%29%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...expand\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y%28-16y%29-4%28-1%29%3E=0 ALIGN=MIDDLE  ALT=\"-4y%28-16y%29-4%28-1%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=64y%5E2%2B4%3E=0 ALIGN=MIDDLE  ALT=\"64y%5E2%2B4%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=16y%5E2%2B1%3E=0 ALIGN=MIDDLE  ALT=\"16y%5E2%2B1%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it will be for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E0 ALIGN=MIDDLE  ALT=\"y%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=1%2F16 ALIGN=MIDDLE  ALT=\"y%3C=1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<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 of <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=1%2F16 ALIGN=MIDDLE  ALT=\"y%3C=1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E0 ALIGN=MIDDLE  ALT=\"y%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > } </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );