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

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


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%283x%5E2-4x%2B3%29%2F%28x%2B2%29+=+3x-10+%2B+23%2F%28x%2B2%29, 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(20059) About Me  (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)? 

%22f%28x%29%22%22%22=%22%22%283x%5E2-4x%2B3%29%2F%28x%2B2%29


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

%22f%28x%29%22%22%22=%22%22green%283x-10%29red%28%22%22%2B%22%22%29red%2823%2F%28x%2B2%29%29
  
That red fraction becomes very small when x is very large in absolute
value.  For instance when x = 1000000, the red fraction red%2823%2F%28x%2B2%29%29
becomes red%2823%2F%28x%2B2%29%29 becomes .0000223 which is very near zero.  And also,
when x = -1000000, the red fraction red%2823%2F%28x%2B2%29%29 becomes -.000023 which is very near zero.


That means

%22f%28x%29%22%22%22=%22%22green%283x-10%29red%28%22%22%2B%22%22%29red%2823%2F%28x%2B2%29%29

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

y%22%22=%22%22green%283x-10%29

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

equation is

y = 3x - 10

 

Edwin