document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175742>Question 1175742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the given rational function f(x) = 3 - 3x over (divided by) x - 5, find the following\r<BR>\n" );
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document.write( "A) Find the intercepts for the graph.<BR>\n" );
document.write( "B) Determine the domain.<BR>\n" );
document.write( "C) Find any vertical or horizontal asymptotes for the graph.<BR>\n" );
document.write( "D) Sketch any asymptotes as dashed lines. Then sketch a graph of y = ​f(x).\r<BR>\n" );
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document.write( "Homework question from Hans  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801438 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=801438\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation is:\r<BR>\n" );
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document.write( "(3 - 3x) / (x - 5)\r<BR>\n" );
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document.write( "the equation will have a vertical asymptote at x = 5 because, when the value of x is equal to 5, the equation becomes -12 / 0 which is undefined.\r<BR>\n" );
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document.write( "as x approaches 5 from the left, the equation will get more and more positive.<BR>\n" );
document.write( "as x approaches 5 from the right, the equation will get more and more negative.\r<BR>\n" );
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document.write( "for example, when x = 4.999, the equation becomes (3 - 3*4.999) / (4.999 - 5)  = 11997 which is a positive value, and when x = 5.0001, the equation becomes (3 - 3 * 5.001) / 5.001 - 50 = -12003.\r<BR>\n" );
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document.write( "the closer you get to 5 from the left, the value of y becomes larger and larger in a positive direction.\r<BR>\n" );
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document.write( "the closer you get to 5 from the right, the value of y becomes larger andlarger in a negative direction.\r<BR>\n" );
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document.write( "the vertical asymptote ia at x = 5, where the value of y is undefined.\r<BR>\n" );
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document.write( "to find the horizontal asymptote, you need to let the value of x get larger and larger in both direction, i.e larger in a positive direction and larger and larger in a negative direction.\r<BR>\n" );
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document.write( "if you pick a large enough value, you will see that, as x gets larger and larger in a negative direction, y approaches the value of - 3 from a value of y that is less negative than -3, and as x gets larger and larger in a positive direction, y approaches the value of - 3 from a value of y that is more negative than -3.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "when x = 100,000, the value of y is equal to (3 - 3 * 100,000) / (100,000 - 5) = -3.0001.....\r<BR>\n" );
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document.write( "when x = -100,000, the value of y is equal to (3 - 3 * -100,00) / (-100,000 - 5) = -2.99988.....\r<BR>\n" );
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document.write( "this can be seen in the following graphs.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/022302.jpg\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/022303.jpg\" >\r<BR>\n" );
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document.write( "the first graph shows you the vertical asymptote at x = 5.\r<BR>\n" );
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document.write( "the second graph shows you the horizontal asymptote at y = -3.\r<BR>\n" );
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document.write( "here's a reference by purplemath.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/asymtote.htm\" target = \"_blank\">https://www.purplemath.com/modules/asymtote.htm</a>\r<BR>\n" );
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document.write( "there are 4 sections to that tutorial.\r<BR>\n" );
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document.write( "the first is vertical asymptotes.<BR>\n" );
document.write( "the second is horizontal asymptotes.<BR>\n" );
document.write( "the third is slant asymptotes.<BR>\n" );
document.write( "the fourth is examples.\r<BR>\n" );
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document.write( "all are very good, but for your problem, you may want to concentrate on vertical and horizontal since your problem doesn't encounter slant asymptotes.\r<BR>\n" );
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