document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189950>Question 189950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "I will first write the task and then what I have tried!\r<BR>\n" );
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document.write( "f(x)=(3x^2-3)/x^2-16)\r<BR>\n" );
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document.write( "(a) Find the domain.\r<BR>\n" );
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document.write( "(- infinity, -4) U (-4,4) U (4, infinity)\r<BR>\n" );
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document.write( "(b) Determine the vertical asymptote(s).\r<BR>\n" );
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document.write( "x= -4 and x= 4, those are the vertical asymptotes!\r<BR>\n" );
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document.write( "(c) Determine the horizontal asymptote or oblique asymptote. \r<BR>\n" );
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document.write( "Y = 3/1\r<BR>\n" );
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document.write( "The numerator is dominated by 3x2 and the denominator is dominated by x2\r<BR>\n" );
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document.write( "Since it states P(x)/Q(x), it must be 3/1\r<BR>\n" );
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document.write( "(d)  Find the y-intercept.\r<BR>\n" );
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document.write( "(e) Find the x-intercept(s).\r<BR>\n" );
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document.write( "I tried a-c and hope it is correct, but I don't know how to find the intercepts with this number or I am just confused since we have done intercepts at the beginning of the semester...\r<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 #142521 by </B><A HREF=/tutors/aboutme.mpl?userid=cutepiscean5><B>cutepiscean5(19)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=cutepiscean5><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=142521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have the given function as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=%283x%5E2-3%29%2F%28x%5E2-16%29+ ALIGN=MIDDLE  ALT=\"+f%28x%29=%283x%5E2-3%29%2F%28x%5E2-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( ">>> (a) Find the domain.\r<BR>\n" );
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document.write( ">>> (- infinity, -4) U (-4,4) U (4, infinity) ----- This is perfect and correct.\r<BR>\n" );
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document.write( ">>> (b) Determine the vertical asymptote(s).\r<BR>\n" );
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document.write( ">>> x= -4 and x= 4, those are the vertical asymptotes! --- Correct\r<BR>\n" );
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document.write( ">>> (c) Determine the horizontal asymptote or oblique asymptote. \r<BR>\n" );
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document.write( ">>>> Y = 3/1 -------- Correct\r<BR>\n" );
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document.write( "The numerator is dominated by 3x2 and the denominator is dominated by x2\r<BR>\n" );
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document.write( "Since it states P(x)/Q(x), it must be 3/1\r<BR>\n" );
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document.write( ">>>> (d)  Find the y-intercept.\r<BR>\n" );
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document.write( "To find the y-intercept we plug in x=0 in the equation. The concept of x and y-intercepts is that, when the graph/curve/function crosses the x-axis, it cuts t x-axis at some point (a,0), this point is known as the x-intercept, here y-coordinate=0. Similar is the case for y-intercepts. when the curve cuts the y-axis at (0,b) the x-coordinate =0 and this point is known as the y-intercept.\r<BR>\n" );
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document.write( "so, to find the y-intercept, we put x=0, we have: (here y = f(x))\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+%283%280%29%5E2-3%29%2F%28%280%29%5E2-16%29+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+%283%280%29%5E2-3%29%2F%28%280%29%5E2-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+-3%2F%28-16%29+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+-3%2F%28-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+3%2F16+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+3%2F16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so we have the y-intercept as (0,3/16)\r<BR>\n" );
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document.write( "(e) Find the x-intercept(s).\r<BR>\n" );
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document.write( "so, to find the x-intercept, we put y=0, we have: (here y = f(x))\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+%283x%5E2-3%29%2F%28x%5E2-16%29+ ALIGN=MIDDLE  ALT=\"+0+=+%283x%5E2-3%29%2F%28x%5E2-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+3x%5E2-3+ ALIGN=MIDDLE  ALT=\"+0+=+3x%5E2-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%5E2+=+3+ ALIGN=MIDDLE  ALT=\"+3x%5E2+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (divide this equation by 3)<BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+=+1+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=>  x = +1 or x = -1 (after taking the square root)<BR>\n" );
document.write( "so we have the x-intercepts as (-1,0) and (1,0)\r<BR>\n" );
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document.write( ">>>I tried a-c and hope it is correct, but I don't know how to find the >>>intercepts with this number or I am just confused since we have done >>>intercepts at the beginning of the semester...\r<BR>\n" );
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document.write( "Good Luck \r<BR>\n" );
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