SOLUTION: What is the slant asymptote for the function f(x)=(3x^2-4x+3)/(x+2)?

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Question 389527: What is the slant asymptote for the function f(x)=(3x^2-4x+3)/(x+2)?
Found 2 solutions by robertb, Edwin McCravy:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
, after long division of polynomials. The slant aymptote is exactly the quotient 3x - 10. The equation of the slant asymptote thus is y = 3x-10.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
What is the slant asymptote for the function f(x)=(3x^2-4x+3)/(x+2)? 




Rewrite the function by dividing out the expression on the right
by long division:

            3x - 10
x + 2)3x² - 4x +  3
      3x² + 6x
          -10x +  3
          -10x - 20
                 23


  
That red fraction becomes very small when x is very large in absolute
value.  For instance when x = 1000000, the red fraction 
becomes  becomes .0000223 which is very near zero.  And also,
when x = -1000000, the red fraction  becomes -.000023 which is very near zero.


That means



gets closer and closer to just being equal to the green part:



Here is the graph:. The green line is the slant asymptote, whose

equation is

y = 3x - 10

 

Edwin
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