document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468508>Question 468508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Showing your work at each step, analyze the graph of the following function by completing the following parts: <BR>\n" );
document.write( "(A)Determine the x- and y-intercepts of the graph. Write them as points. <BR>\n" );
document.write( "(B)Determine the domain and vertical asymptotes, if any, of the function. <BR>\n" );
document.write( "(C)Write the domain in interval notation. <BR>\n" );
document.write( "(D)Determine the horizontal or oblique asymptote, if any, of the function. <BR>\n" );
document.write( "(E)Obtain additional points on the graph. You should use a table to show your work in finding the additional points. <BR>\n" );
document.write( "(F)Plot the x- and y-intercepts, the additional points, and the asymptotes that you found on a rectangular coordinate system and graph the function. Draw the asymptotes using dashed lines. <BR>\n" );
document.write( " <BR>\n" );
document.write( "f(x)=x²-2x-8/x-1\r<BR>\n" );
document.write( "\n" );
document.write( "Oh my goodness can someone please help me with this monster problem! PLEASE!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321497 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=321497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Showing your work at each step, analyze the graph of the following function by completing the following parts: <BR>\n" );
document.write( "(A)Determine the x- and y-intercepts of the graph. Write them as points. <BR>\n" );
document.write( "(B)Determine the domain and vertical asymptotes, if any, of the function. <BR>\n" );
document.write( "(C)Write the domain in interval notation. <BR>\n" );
document.write( "(D)Determine the horizontal or oblique asymptote, if any, of the function. <BR>\n" );
document.write( "(E)Obtain additional points on the graph. You should use a table to show your work in finding the additional points. <BR>\n" );
document.write( "(F)Plot the x- and y-intercepts, the additional points, and the asymptotes that you found on a rectangular coordinate system and graph the function. Draw the asymptotes using dashed lines. \r<BR>\n" );
document.write( "\n" );
document.write( "f(x)=x²-2x-8/x-1<BR>\n" );
document.write( "...<BR>\n" );
document.write( "I will not be able to draw you a detailed graph because I don't know how to do this with this format, but I should provide you with the information you need to draw the graph yourself.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "f(x)=x²-2x-8/x-1<BR>\n" );
document.write( "Since the numerator is one degree higher than the degree of the denominator, given function has a slant or oblique asymptote.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(A) Intercepts:<BR>\n" );
document.write( "x-intercept: set y=0, then solve for x. In effect, you are setting the numerator=0.<BR>\n" );
document.write( "x²-2x-8=0<BR>\n" );
document.write( "(x-4)(x+2)=0<BR>\n" );
document.write( "x-4=0<BR>\n" );
document.write( "x=4<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x+2=0<BR>\n" );
document.write( "x=-2<BR>\n" );
document.write( "x-intercepts: (4,0) and (-2,0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y-intercept: set x=0, then solve for y<BR>\n" );
document.write( "f(0)=x²-2x-8/x-1<BR>\n" );
document.write( "f(0)=-8/-1=8<BR>\n" );
document.write( "y-intercept: (0,8)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(B),(C)&(D) Domain and asymptotes:\r<BR>\n" );
document.write( "\n" );
document.write( "Domain: set denominator=0, then solve for x<BR>\n" );
document.write( "x-1=0<BR>\n" );
document.write( "x&#8800;1<BR>\n" );
document.write( "Domain:(-&#8734;,1) U (1,&#8734;)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "vertical asymptote: set denominator=0, then solve for x.<BR>\n" );
document.write( "x-1=0<BR>\n" );
document.write( "x=1<BR>\n" );
document.write( "vertical asymptote: x=1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "slant asymptote: by long division, divide numerator by denominator. You will get a quotient plus a remainder. The quotient is the equation of the slant asymptote, a straight line.<BR>\n" );
document.write( "x²-2x-8/x-1=(x-1)+Remainder,-9/(x-1). Equation of the slant asymptote: y=x-1<BR>\n" );
document.write( "There are no horizontal asymptotes<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(E) & (F) Graphing:<BR>\n" );
document.write( "See the graph below as a visual check on the answers above. It will give you a good idea what your curve should look like. You can get additional points to plot the graph by plugging in different x-values. Note that the slant asymptote is a straight line with a slope of 1 and a y-intercept of -1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=(x-4)(x+2)/(x-1)<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );