document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91297>Question 91297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given: F(x) = x/x^2-9 <BR>\n" );
document.write( "a. Find the x-intercept(s).<BR>\n" );
document.write( "b. Find the y-intercept(s).<BR>\n" );
document.write( "c. Find the vertical asymptote(s) (write as an equation of a line).<BR>\n" );
document.write( "d. Find the horizontal asymptote(s) (write as an equation of a line).<BR>\n" );
document.write( "e. For x<-3, is there a value which F(x) cannot exceed, AND/OR a value which F(x) cannot fall below? Explain your answers.<BR>\n" );
document.write( "f. Is the function increasing or decreasing in the interval -3<- x <- 3?<BR>\n" );
document.write( "g. As x approaches 3 from the left, what happens to the function values?<BR>\n" );
document.write( "h. As x approaches 3 from the right, what happens to the function values? <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66274 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=66274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given: F(x) = x/x^2-9 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%2F%28x%5E2-9%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%2F%28x%5E2-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a. Find the x-intercept(s).<BR>\n" );
document.write( "Let y=0 and solve for x; y is 0 when the numerator is 0, i.e. when x=0<BR>\n" );
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document.write( "b. Find the y-intercept(s).<BR>\n" );
document.write( "Let x = 0, they y = 0<BR>\n" );
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document.write( "c. Find the vertical asymptote(s) (write as an equation of a line).<BR>\n" );
document.write( "Let x^2-9=0 then x=3 of x=-3; these are the vertical asymptotes.<BR>\n" );
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document.write( "d. Find the horizontal asymptote(s) (write as an equation of a line).<BR>\n" );
document.write( "The coefficients of the highest power term in the numerator and in the<BR>\n" );
document.write( "denominator are 0/1; The horizontal asymptote is y=0<BR>\n" );
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document.write( "e. For x<-3, is there a value which F(x) cannot exceed, AND/OR a value which F(x) cannot fall below? Explain your answers.<BR>\n" );
document.write( "You know the horizontal asymptote is y=0.  Take a test value like x=-5<BR>\n" );
document.write( "to see where the graph is relative to the line y=0.<BR>\n" );
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document.write( "f. Is the function increasing or decreasing in the interval -3<- x <- 3?<BR>\n" );
document.write( "Take a look at the graph.<BR>\n" );
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document.write( "g. As x approaches 3 from the left, what happens to the function values?<BR>\n" );
document.write( "Check the graph<BR>\n" );
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document.write( "h. As x approaches 3 from the right, what happens to the function values?<BR>\n" );
document.write( "Check the graph<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );