You can put this solution on YOUR website! graph the following rational function: R(x)=x^2+14x+24/x^2+13x+12
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R(x)=x^2+14x+24/x^2+13x+12
R(x)=(x+12)(x+2)/(x+12)(x+1)
R(x)=(x+2)/(x+1)
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Horizontal asymptote:
If degree of numerator and denominator equal, divide leading coefficient of top by leading coefficient of bottom. The quotient is the horizontal asymptote. In this case HA=1/1=1
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Vertical asymptote:
Set denominator=0, then solve for x
x+1=0
x=-1 (vertical asymptote)
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y-intercept
set x=0, then solve for y
y=(0+2)/(0+1)=2 (y-intercept)
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x-intercepts
set y=0, then solve for x by setting numerator=0
x+2=0
x=-2
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number line with critical points:
<...+...-2.....-.....-1.....+......>
You now have all the information you need to plot the graph.
see graph below as a visual check on what the curve should look like
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