posted by .

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 asymptote at x = -1 and a horizontal asymptote at y =2

e) an oblique asymptote, but no vertical asymptote

  • Precalculus -

    a) must have (x-1) in numerator and denominator

    y = (x-2)(x-1)/(x-1) = (x^2 - 3x + 1)/(x-1)

    b) must have (x-k) in the denominator, and not in the numerator. degree of numerator must be less than the degree of the denominator.

    y = 12(x+3)/(x-5)(x+9)

    c) must have (x+2) top and bottom, and have (x-1) in the bottom

    y = 3(x+5)(x+2)/(x-1)(x+2) = (3x^2 + 21x + 18)/(x^2 + x - 2)

    d) must have (x+1) in the bottom and have degree of top and bottom equal, with a factor of two up top.

    y = (2x-5)/(x+1)

    e) top degree must be bottom degree + 1

    y = 3x^3/(x^2+3)
    note the bottom is never 0.

  • Precalculus - PS -

    a) should read (x^2 - 3x + 2)/(x-1)

    c) should read (3x^2 + 21x + 30)/(x^2 + x - 2)

  • Precalculus -

    what is the rational equation of a function with intercepts at (8,0) and (0,0.16) and a horizontal asymptote at y=0.5 and a vertical asymptote at x=3 and a removable discontinuity at (3,-1)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Analyze the function algebraically. List its vertical asymptotes, holes, y-intercept, and horizontal asymptote, if any. q(x)= -4/x-2 vertical asymptote= hole= horizontal asymptote= y-intercept=
  2. ****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 …
  3. Pre-Calculus

    Rational Functions does the following function have a hole or a vertical asymptote or both?
  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
  5. Algebra - Help!

    Given the function: f(x)=(x^2+6x+5)/(x^2+3x−10) Find the Domain: Vertical asymptote(s): Hole(s): Horizontal asymptote (if exists):
  6. 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
  7. math

    Describe the vertical asymptote(s) and hole(s) for the graph of .y=(x-3)(x-1)/(x-1)(x-5) A. asymptote: x = 5 and hole: x = 1 B. asymptote: x = –5 and hole: x = –1 C. asymptote: x = –3 and hole: x = 5 D. asymptote: x = 5 and hole: …
  8. 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 through …
  9. Math(Please help!)

    Describe the vertical asymptote and hole for the graph of (x^2+x-6)/(x^2-9). a. asymptote: x=2; hole: x=-3 b. asymptote: x=3; hole: x=2 c. asymptote: x=-3; hole: x=3 d. asymptote: x=3; hole: x=-3 I know that it has to either be b or …
  10. Algebra

    Determine the holes, vertical asymptotes and horizontal asymptotes of the rational function y=(3x^(2)+8x-10)/(x^(2)+7x+12) Hole: Vertical Asymptote: Horizontal Asymptote:

More Similar Questions