Question 561096
 y= x^2+7x+10
....._________
.....x^2+17+16 
find vertical asymptotes horizontal asymptotes, roots , y-intercept and sketch the graph 
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Horizontal asymptote: y = x^2/x^2 = 1
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Factor to find vertical asymptotes:
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y = [(x+2)(x+5)]/[(x+16)(x+1)]
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Vertical asymptotes where x = -16 and where x = -1.
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Roots:
Let y = 0 and solve for "x":
The fraction will be zero when x = -2 and when x = -5.
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y-intercept:
Let x = 0, then y = (10)/(16) = 5/8
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Sketch:
{{{graph(400,400,-40,20,-20,10,((x+2)(x+5))/((x+16)(x+1)))}}}
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Cheers,
Stan H.