document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=404675>Question 404675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=4/3x+5   What is the domain and range? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #286084 by </B><A HREF=/tutors/aboutme.mpl?userid=neatmath><B>neatmath(302)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=neatmath><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=neatmath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=286084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><font face=\"Tahoma\">If the function you are asking about is <br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%284%2F3%29%2Ax%2B5 ALIGN=MIDDLE  ALT=\"f%28x%29=%284%2F3%29%2Ax%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "then it is easy to see that there are no possible discontinuities.<br>\r<BR>\n" );
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document.write( "When we speak of discontinunities, we are looking for values of x where f(x) is not defined.<br>\r<BR>\n" );
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document.write( "The best examples of these are when you end up with zero in the denominator, or when you have the square root of a negative number.<br>\r<BR>\n" );
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document.write( "So without any visible discontinuities, we can see that the domain of f(x) is ALL REAL NUMBERS.<br>\r<BR>\n" );
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document.write( "The range of f(x) is also ALL REAL NUMBERS for the same reasoning.<br>\r<BR>\n" );
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document.write( "However, if the function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=4%2F%283x%29%2B5 ALIGN=MIDDLE  ALT=\"f%28x%29=4%2F%283x%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "then we can see a potential discontinuity when x=0<br>\r<BR>\n" );
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document.write( "When x=0, we have 0 in the denominator which is not allowed.<br>\r<BR>\n" );
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document.write( "So the domain of that function would be ALL REAL NUMBERS except 0.<br>\r<BR>\n" );
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document.write( "The range of that function would be ALL REAL NUMBERS except 5.<br>\r<BR>\n" );
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document.write( "When you ask a question, be very careful of how you \"group\" the variables and numbers.<br>\r<BR>\n" );
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document.write( "From the original question, it is hard to tell if the function you are asking about is<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%284%2F3%29%2Ax%2B5 ALIGN=MIDDLE  ALT=\"f%28x%29=%284%2F3%29%2Ax%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=4%2F%283x%29%2B5 ALIGN=MIDDLE  ALT=\"f%28x%29=4%2F%283x%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "I hope this helps!   :)<br> </SPAN>\n" );
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