document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019976>Question 1019976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help solve this question.<BR>\n" );
document.write( "	Consider the function  <BR>\n" );
document.write( "f(x)=(x^2-1)/(x-3)<BR>\n" );
document.write( "	a. Find the domain for the function in interval notations<BR>\n" );
document.write( "	b. Find all vertical, horizontal and slant asymptotes<BR>\n" );
document.write( "	c. Sketch the function<BR>\n" );
document.write( "	d. Solve the inequality  <BR>\n" );
document.write( "  (x^2-1)/(x-3)<1<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635927 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=635927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\"><BR>\n" );
document.write( "The domain of a function is the set of values of the independent variable for which the function is defined.  For a rational function such as your example, that means the set of all real numbers except for those values that cause the denominator to equal zero.\r<BR>\n" );
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document.write( "The equation of a vertical asymptote is of the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ a\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> is a value that causes the denominator function to equal zero, but does NOT cause the numerator function to be zero.  If both numerator and denominator go to zero at a value, then the rational function has a discontinuity or \"hole\" at that point, but there is no asymptote.\r<BR>\n" );
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document.write( "If the degree of the numerator polynomial in a rational function is LESS than the degree of the denominator function, the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-axis is the horizontal asymptote.  If the degree of the numerator polynomial is EQUAL to the degree of the denominator polynomial, then the equation of the horizontal asymptote is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ \frac{a}{b}\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> is the lead coefficient of the numerator polynomial and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> is the lead coefficient of the denominator polynomial.  If the degree of the numerator polynomial is GREATER than the degree of the denominator polynomial then there is a slant (aka oblique) asymptote with an equation <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ Q(x)\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large Q(x)\"> is the quotient excluding the remainder when the denominator polynomial is divided into the numerator polynomial using polynomial long division.\r<BR>\n" );
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document.write( "a.  Set the denominator equal to zero and solve.  The domain is the set of real numbers excluding this(these) value(s).\r<BR>\n" );
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document.write( "b.  Evaluate the numerator for the value(s) excluded from the domain in part a.  If the numerator is NOT zero for a tested value, then there is a vertical asymptote at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> equal to that value.  Since your numerator has a degree larger than the degree of your denominator, there is no horizontal asymptote.  Use polynomial long division to determine the equation of the slant asymptote.  If you need a refresher, click <a  rel=nofollow HREF=\"http://www.purplemath.com/modules/polydiv2.htm\">Purple Math Polynomial Long Division</a>.  Be sure to read all of the relevant pages.\r<BR>\n" );
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document.write( "c. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solver91311&illustration_name=rationalfunctionNGTD.jpg\">\r<BR>\n" );
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document.write( "d.  By inspection of the graph.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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