Math

posted by .

How do you find the vertical and horizontal assymptotes of the graph of the rational function?

f(x)= 3x^2-5x+2/6x^2-5x+1

f(x)= 2x+3/(ãx^2-2x+3)

  • Math:use parentheses -

    Vertical asymptotes in rational functions usually come from the denominator approaching zero.
    In
    f(x)= (3x^2-5x+2)/(6x^2-5x+1)
    the denominator can be factorized as:
    (3x-1)(2x-1)
    at x=1/3 or x=1/2, the denominator becomes zero, and hence a vertical asymptote. You also need to check if the numerator vanishes at the same points, in which case the point will be undefined.

    To find the horizontal asymptotes, do a long division, and the resulting leading constant (1/2) is the horizontal asymptote. Take care to determine from which side of y=1/2 the curve approaches the asymptote as x approaches ±∞.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. graph from asymptotes

    Is it possible to roughly sketch a graph(without plotting the points) from the asymptotes of a rational function?
  2. 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 function. …
  3. math (calculus) PLZZZ help!

    Consider the function below. (Round the answers to two decimal places. If you need to use - or , enter -INFINITY or INFINITY.) f(x) = e^x/1+e^x find the horizontal and vertical assymptotes?
  4. ****college algebra…radical functions****

    Create a rational function such that the graph of has vertical asymptotes at x=5 and x= -7, a hole at x=2 , and a horizontal asymptote at y = 14. By creating a rational function, you are to write rule for this function. There are many …
  5. precalculus

    How do I find the vertical/horizontal compression/stretch?
  6. Math

    Verify these answers :] Would be thankies~ 1. Determine the intervals in which the reciprocal function of f(x)= x^2+1 is increasing. a) (0,∞) b) (-∞, 0) c) (-∞,∞) d) (1,∞) Answer: D -------------------------------------- …
  7. College Algebra

    1.Use completing the square to describe the graph of the following function. Support your answer graphically. f(x) = -2x^2 + 4x + 5 2. Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function. …
  8. College Algebra HELP

    Use the seven step method described in the book to graph the following rational function f(x)=(2x^2+x-3)/(2x^2-7x) 1) Determine the symmetry of the function 2) Find the y-intercept 3) Find the x-intercept 4) Find the vertical asymptotes …
  9. Algebra

    Graph the rational function x/(x-6) To graph the function, draw the horizontal and vertical asymptotes (if any) and plot at least two points on each piece of the graph.
  10. Math

    Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label …

More Similar Questions