calculus

posted by .

Determine if the graph of the rational function has a slant asymptote. If it does, find the equation of the slant asymptote.


(2x^3+18x^2+47x+24)/(x^2+6x+5)

  • calculus -

    As x gets very large in magnitude this looks like
    2 x^3/x^2
    or in other words 2x
    line with slope of 2
    y = 2x

  • calculus -

    Oh, when x = 0
    y = 24/5
    so
    y = 2 x + 24/5

  • calculus -

    So a long division to get

    (2x^3 + 18x^2 + 47x + 24)/ (x^2 + 6x + 5) = 2x + 6 + (x-6)/(x^2+6x+5)

    so as x get larger, (x-6)/(x^2+6x+5)
    ---> 0
    and we are left with
    y = 2x + 6

    So the slant asymptote is y = 2x + 6

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre Cal.

    Determine the slant asympotte [sic] for f (x) = (x^2 - 5x - 3)/x My answer: (x^2 - 5x - 3)/x = x - 5 - 3/x The slant asymptote is y = x - 5.
  2. Calculus

    Which of these rational functions has a ) horizontal asymptote?
  3. calculus

    f(x) = (9x^3 - 1x^2 + 8x + 4)/(-2x^2 - 4x - 2) What is the smallest value of x at which f(x) intersects its non-vertical asymptote?
  4. Trigonometry

    F(X) = 2x^3-5x^2-19x+1 / x^2-9....I need the vertical asymptote, horizontal asymptote and the slant asymptote...please help!
  5. Algebra

    Graph and label the following two functions: f(x)=(x^2+7x+12)/(x+4) g(x)=(-x^2+3x+9)/(x-1) 1. Describe the domain and range for each of these functions. 2. Determine the equation(s) of any asymptotes found in the graphs of these functions, …
  6. algebra

    find the slant asymptote of the graph of the rational function and use the slant asymptote to graph. f(x)=x^2+x-2/x-7 find slant asymptote of graph of f use slant asymptote to graph rational function find x and y intercepts find vertical …
  7. pre-cal

    what is the slant asymptote of the graph of the rational function and b use the slant to graph the rational function. f(x)x^2-x-20/x-6 a. y=?
  8. College Algebra

    3x-1/x^2-10x+26 Find all (real) zeros of the function Find all (real) poles of the function The function has... A horizontal asymptote at 0?
  9. pre calculus

    use the seven step method to graph the following rational function: f(x)=3x^2+x-4/2x^2-5x a. determine the symmetry of the function. b. find the x and y intercepts. c. find the verticle asymptote d.find the horizontal asymptote e.plot …
  10. Math

    Write a rational function satisfying the following criteria. vertical Asymptote: x=-1, slant asymptote: y=x+2, zero of the function: x=3 I had f(x)=x^2+3x+2/x+1, that only works for the asymptotes and not the zero can someone please …

More Similar Questions