SOLUTION: Find the intercepts, asymptotes, use limits to describe the behavior at the vertical asymptotes and analyze and draw the graph of f(x)=(x+1)/(x^2-3x-10)

Algebra ->  Algebra  -> Graphs -> SOLUTION: Find the intercepts, asymptotes, use limits to describe the behavior at the vertical asymptotes and analyze and draw the graph of f(x)=(x+1)/(x^2-3x-10)      Log On

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Question 295155: Find the intercepts, asymptotes, use limits to describe the behavior at the vertical asymptotes and analyze and draw the graph of f(x)=(x+1)/(x^2-3x-10)
Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
To find the y-intercept, set x=0 and solve for y.
f%280%29=%280%2B1%29%2F%280%5E2-3%280%29-10%29=1%2F-10=-1%2F10
(0,-1/10)
To find the x-intercept, set y=0 and solve for x.
0=%28x%2B1%29%2F%28x%5E2-3x-10%29
x%2B1=0
x=-1
(-1,0)
To find vertical asymptotes, look for x where the denominator goes to zero.
x%5E2-3x-10=0
%28x%2B2%29%28x-5%29=0
Two solutions:
x%2B2=0
x=-2
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x-5=0
x=5
To find horizontal asymptotes, divide all terms by the highest order of x.
f%28x%29=%28x%2Fx%5E2%2B1%2Fx%5E2%29%2F%28x%5E2%2Fx%5E2-3x%2Fx%5E2-10%2Fx%5E2%29
f%28x%29=%281%2Fx%2B1%2Fx%5E2%29%2F%281-3%2Fx-10%2Fx%5E2%29
Now take the limit as x goes to infinity.
lim%28+x-%3E-infinity%2C+f%28x%29+%29=%280%2B0%29%2F%281-0-0%29=0
So there is a horizontal asymptote at y=0.
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