document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980068>Question 980068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the discontinuiny, and the zeros of the function for f(x) = the quantity negative x squared plus x plus 20 over the quantity x plus 4 (-x^2+x+20/x+4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601312 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the discontinuity of the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%5E2%2Bx%2B20%29%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%28-x%5E2%2Bx%2B20%29%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we will look at the denominator and determine what value for x will result in the denominator equalling 0, since the denominator cannot equal 0.  To do this, we will set our denominator equal to 0:\r<BR>\n" );
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document.write( "x + 4 = 0\r<BR>\n" );
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document.write( "Subtract 4 from both sides, giving us:\r<BR>\n" );
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document.write( "x = -4\r<BR>\n" );
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document.write( "Therefore, our discontinuity is x = -4\r<BR>\n" );
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document.write( "To find our zeroes, we will set our function equal to 0:\r<BR>\n" );
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document.write( "Next, multiply both sides of the equation by (x + 4) to rid ourselves of our fraction on the left side of the equal sign.  This will result in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2Bx%2B20=0 ALIGN=MIDDLE  ALT=\"-x%5E2%2Bx%2B20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Third, multiply the entire equation by -1 to make the equation easier to factor.  This will give us:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-20=0 ALIGN=MIDDLE  ALT=\"x%5E2-x-20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Fourth, factor the left side of the equation.  This will result in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%28x%2B4%29=0 ALIGN=MIDDLE  ALT=\"%28x-5%29%28x%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Set each set of parentheses equal to zero and solve for x:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29=0 ALIGN=MIDDLE  ALT=\"%28x-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we have determined that -4 is NOT a zero since it will result in a zero value in our denominator, our only zero is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can verify by substituting the x in our original equation with 5:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%285%5E2%29%2B%28-5%29%2B20%29%2F%285%2B4%29=0 ALIGN=MIDDLE  ALT=\"%28-%285%5E2%29%2B%28-5%29%2B20%29%2F%285%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-25-5%2B20%29%2F9=0 ALIGN=MIDDLE  ALT=\"%28-25-5%2B20%29%2F9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F9=0 ALIGN=MIDDLE  ALT=\"0%2F9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a true statement, 5 is, in fact, the zero of our function. </SPAN>\n" );
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