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how to graph this rational function x^2+4/x-1
\n" ); document.write( "**
\n" ); document.write( "Since the degree of the numerator is one more than the degree of the denominator, you will get a slant asymptote.
\n" ); document.write( "..
\n" ); document.write( "Slant asymptote:
\n" ); document.write( "Divide numerator by the denominator by long division:
\n" ); document.write( "(x^2+4)/(x+1)=(x+1) + remainder 5/(x-1)
\n" ); document.write( "Slant asymptote: y=x+1 (A straight line with slope=1 and y-intercept=1)
\n" ); document.write( "..
\n" ); document.write( "Vertical asymptote:
\n" ); document.write( "set denominator=0, then solve for x.
\n" ); document.write( "x-1=0
\n" ); document.write( "x=1
\n" ); document.write( "Vertical asymptote: x=1
\n" ); document.write( "..
\n" ); document.write( "y-intercept:
\n" ); document.write( "set x=0
\n" ); document.write( "x^2+4/x-1
\n" ); document.write( "f(0)=-4
\n" ); document.write( "..
\n" ); document.write( "x-intercept
\n" ); document.write( "set y=0
\n" ); document.write( "x^2+4=0
\n" ); document.write( "x^2=-4
\n" ); document.write( "no solution
\n" ); document.write( "x-intercept: none
\n" ); document.write( "..
\n" ); document.write( "number line:
\n" ); document.write( "<....-.....1....+.......>
\n" ); document.write( "You now have the following parameters to plot given rational function:
\n" ); document.write( "Slant asymptote:y=x+1
\n" ); document.write( "Vertical asymptote: x=1
\n" ); document.write( "Horizontal asymptote: none
\n" ); document.write( "y-intercept: -4
\n" ); document.write( "x-intercept: none
\n" ); document.write( "see the graph below as a visual check on the above
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