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