Which of these rational functions has a ) horizontal asymptote? a slant asymptote? no vertical asymptote?

r(x)= 2x-1/ x^2-x-2 = 2x-1/ (x-2)(x+1)
s(x)= x^3+27/x^2+4 = (x+3)(x^2-3x+9)/(x-2)(x+2)
t(x)=x^3-9x= x(x-3)(x+3)/x+2
u(x)=x^2+x-6/x^2-25= (x+3)(x-2)/(x+5)(x-5)

I do not know how to determine the asymptotes. Please help me. I would sincerely appreciate it. Thanks!

  1. 👍
  2. 👎
  3. 👁
  1. Vertical asymptotes are typically present in functions with a polynomial denominator. The vertical asymptote is located where the value of x is such that the denominator is zero. If the denominator is not a polynomial, the same applies whenever the denominator becomes zero.

    To find horizontal asymptotes, you would divide the polynomials by long division.
    If the result is of the form p+q/P(x), where p and q are integers and P(x) is a polynomial, the horizontal asymptote is y=p, since the second term vanishes when P(x) becomes infinity.

    If the result of the long division is px+q+r/P(x), then the line y=px+q is the oblique asymptote, again, the last term vanishes as x becomes infinity.

    You can conclude that the function has no vertical asymptote when the denominator does not vanish for all real values of x.

    If you need a check on the answers, feel free to post.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Precalculus

    Write an equation for rational function with given properties. a) a hole at x = 1 b) a vertical asymptote anywhere and a horizontal asymptote along the x-axis c) a hole at x = -2 and a vertical asymptote at x = 1 d) a vertical

  2. Calculus

    If the graph of y = (ax - b)/(x - c) has a horizontal asymptote y=5 and a vertical asymptote x = − 2 , then b cannot be equal to what?

  3. Math

    Give an example of a rational function that has vertical asymptote x = 3 and x = -3, horizontal asymptote y = 2 and y-intercept is (0, 4)

  4. Math

    If x=1 is the vertical asymptote and y=-3 is the horizontal asymptote for the graph of the function f which of the following could be the equation of the curve A.f(x)=(-3x^2)/(x-1) B.f(x)=-3(x-1)/(x+3) C.f(x)=-3(x^2-1)/(x-1)

  1. Pre Cal

    which of the following best describes the behavior of thre function f(x)=(x^2-2x)/(x^2-4) at the values not in its domain? a) one vertical asymptote, no removable discontinuities b) 2 vertical asymptotes c) two removable

  2. Rational Functions

    Write an equation for a rational function whose graph has the following properties: x-intercept of 3 y-intercept of -3 vertical asymptote of x=-2 horizontal asymptote of y=2

  3. Calculus AB

    Let f be the function that is given by f(x)=(ax+b)/(x^2 - c). It has the following properties: 1) The graph of f is symmetrical with respect to the y-axis 2) The graph of f has a vertical asymptote at x=2 3) The graph of f passes

  4. advance functions gr12

    write an equation for a rational function whose graph has all of the indicated features: -vertical asymptote with equation x=3 -horizontal asymptote with equation y=2 -hole at x=1 no x intercept thank you

  1. Math

    20. (4 points) Write an equation for a rational function whose graph has all of the indicated features. vertical asymptote with equation x 3 horizontal asymptote with equation y =2 hole at x= 1 no x-intercepts

  2. Mathematics

    A rational function, R(x) has the following characteristics: a vertical asymptote at x = 3, a horizontal asymptote at y = 2, and a hole at (2, −2). Sketch the function and determine what it could be using the following steps:

  3. Algebra

    Enter the equations of the asymptotes for the function f(x) . f(x)= −(2/x+4) − 6 Vertical Asymptote: ? Horizontal Asymptote: ?

  4. Gr.11 - Rational functions graphing.

    1. Identify a rational function whose graph is a horizontal line except for two holes. Graph the function. 2. Identify a rational function who graph lies entirely above the x-axis and has a single vertical asymptote. Graph the

You can view more similar questions or ask a new question.