SOLUTION: Sketch a graph of the rational function y= (x^2+3x+2)/(x^3+4x^2-3x-18) giving exact or numerical values for all intercepts,asymptotes and turning points.

Algebra ->  Linear-equations -> SOLUTION: Sketch a graph of the rational function y= (x^2+3x+2)/(x^3+4x^2-3x-18) giving exact or numerical values for all intercepts,asymptotes and turning points.      Log On


   

Question 352559: Sketch a graph of the rational function
y= (x^2+3x+2)/(x^3+4x^2-3x-18)
giving exact or numerical values for all intercepts,asymptotes and turning points.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=+%28x%5E2%2B3x%2B2%29%2F%28x%5E3%2B4x%5E2-3x-18%29
y=+%28%28x%2B1%29%28x%2B2%29%29%2F%28%28x-3%29%28x%2B2%29%5E2%29
y=+%28%28x%2B1%29%29%2F%28%28x-3%29%28x%2B2%29%29
Vertical asymptotes at x=3 and x=-2.
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%28%28x%2B1%29%29%2F%28%28x-3%29%28x%2B2%29%29=0
x%2B1=0
x=-1
X-intercept is (-1,0).
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y=+%28%28x%2B1%29%29%2F%28%28x-3%29%28x%2B2%29%29
y=+%28%280%2B1%29%29%2F%28%280-3%29%280%2B2%29%29
y=-1%2F6
Y-intercept is (0,-1%2F6)
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y=+%28x%5E2%2B3x%2B2%29%2F%28x%5E3%2B4x%5E2-3x-18%29
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y=+%281%2Fx%2B3%2Fx%5E2%2B2%2Fx%5E3%29%2F%281%2B4%2Fx-3%2Fx%5E2-18%2Fx%5E3%29
As x-%3Einfinity,
y=+%280%2B0%2B0%29%2F%281%2B0-0-0%29
y-%3E0
As x-%3E-infinity, y-%3E0
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