document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206433>Question 206433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State the domain: g(x)= 2x+1 over x-7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155992 by </B><A HREF=/tutors/aboutme.mpl?userid=mickclns><B>mickclns(59)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mickclns><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=155992\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282x%2B1%29+%2F+%28x-7%29+ ALIGN=MIDDLE  ALT=\"+%282x%2B1%29+%2F+%28x-7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28400%2C200%2C-70%2C25%2C-17%2C20%2C++%282x%2B1%29+%2F+%28x-7%29+%29+ ALIGN=MIDDLE  ALT=\"+graph%28400%2C200%2C-70%2C25%2C-17%2C20%2C++%282x%2B1%29+%2F+%28x-7%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "As x gets larger and larger positively or negatively, y will exist (so x will also) and will get close to 2.  However, as x gets closer and closer to 7 the numerator gets closer and closer to 15, but the denominator gets closer and closer to 0, meaning the denominator is tinier and tinier.  But, if you take a number near 15 and divide by a tiny number you get a large (+ or -) number.  For instance, if x = 6.99 then the numerator is 14.98 and the denominator is -0.01 which is the same as -1/100.  <BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%286.99%29+=+14.98%2F-0.01+=+14.98%2A-100+=-1498+ ALIGN=MIDDLE  ALT=\"+g%286.99%29+=+14.98%2F-0.01+=+14.98%2A-100+=-1498+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a huge number, way off the bottom of the graph and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%287.01%29+=+15.02%2F0.01+=+15.02%2A100+=1502 ALIGN=MIDDLE  ALT=\"+g%287.01%29+=+15.02%2F0.01+=+15.02%2A100+=1502\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a huge number, way off the top of the graph.\r<BR>\n" );
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document.write( "Speaking of the graph, near to x = 7, you can see part of the graph that is a vertical line. That shouldn't actually be there. Near to 7 the actual graph just continues farther and farther off the bottom and top of the picture with nothing in the middle (in the picture, where x very near to 7).  If x = 7 then g(7) is 15 / 0, but, since you can't divide by 0, g(7) does not exist, so 7 is not in the domain of g.  All this is to say that the domain of g is ALL REAL NUMBERS EXCEPT FOR 7.<BR>\n" );
document.write( "   -  Mick </SPAN>\n" );
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