document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=588893>Question 588893</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I apologize if this is the wrong section. I just recently got back into school and taking a math course currently and I just got stuck on a question. These type of problems is where I get confused about.\r<BR>\n" );
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document.write( "The problem is:\r<BR>\n" );
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document.write( "Find the range of y=f(x) and graph it.\r<BR>\n" );
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document.write( "f(x){-1/4(x) if x cannot = to 0; -6  if x=0}<BR>\n" );
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document.write( "I appreciate it as this will help me with the next few problems. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #374882 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5396)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=374882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The domain of a function is the set of possible values for x.<BR>\n" );
document.write( "For example the domain for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is all the non-negative x values.<BR>\n" );
document.write( "We may state it as {x: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > }<BR>\n" );
document.write( "The range is the set of all the possible y=f(x) values<BR>\n" );
document.write( "For example the range for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is {y: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=2 ALIGN=MIDDLE  ALT=\"y%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > } because all the values for y=f(x) will be 2 or greater.<BR>\n" );
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document.write( "f(x)=1/(4x)= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%284x%29 ALIGN=MIDDLE  ALT=\"1%2F%284x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a domain of all real numbers except x=0, because when the denominator is zero, the function is undefined; f(0) does not exist.<BR>\n" );
document.write( "The function can be \"patched up\" by defining f(0)=-6, or some such thing.\r<BR>\n" );
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document.write( "The range of that function is all real numbers except y=0 because there is no value for x that maxes f(x)=0. We could fix it by defining f(0)=0, and then the domain and the range would be all real numbers.<BR>\n" );
document.write( "The graph of f(x)=1/(4x) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C+-3%2C3%2C-10%2C10%2C1%2F%284x%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C+-3%2C3%2C-10%2C10%2C1%2F%284x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > If there is a definition \"patch-up\" for x=0, there is an extra point on the y axis. If not patched up, the function never touches the y axis. </SPAN>\n" );
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