Maths

posted by .

f:x -> (4x²-8x-21)/(x²-1)

(a) Analyse
(b) Sketch

I'm struggling on (a) so I can't do (b)
Here are my ideas/what I've got so far:

(a)Domain, x is a set of real numbers; x can not equal 1

Asymptotes x=1, y=?
I think you have to divide here but i can't figure it out with the x² on the bottom.

zeroes: when x=0, y=21
when y=0, x=?
0=4x²-8X-21 then??

extrema; differentiate eqn here...not sure how (maybe convert to another form?)

I think that is all for the analysis?

For any help, thanks in advance

  • Maths -

    where to begin ? ....
    f:x -> (4x²-8x-21)/(x²-1) corresponds to the equation
    y = (4x²-8x-21)/(x²-1)

    for vertical asymptotes, set the denominator equal to zero
    so x^2 - 1 = 0
    (x+1)(x-1) = 0
    x = ± 1
    so there are two vertical asymptotes
    at x = 1 and x = -1

    for horizontal asymptotes, let x ---> ∞

    for very large values of x, the signigicant part of the equation is
    y = 4x^2 / x^2 which approaches 4
    so y = 4 is the horizontal axis

    for x-intercepts, let y = 0
    so (4x²-8x-21)/(x²-1) = 0
    (4x²-8x-21)= 0
    (2x+3)(2x-7) = 0
    x = -3/2 and x = 7/2 are the x-intercepts

    for y -intercepts , let x = 0 in the equation
    so y = (0-0-21)/(0-1) = 21
    so the y-intercept is 21

    Derivative: by quotient rule
    dy/dx = [(x^2-1)(8x-8) - 2x(4x^2-8x-21)]/(x^2 - 1)^2
    expanding the top and setting this equal to zero gave me

    8x^2 + 34x + 8 = 0

    solve this using the quadratic formula to get the x's of the extrema,
    sub those x's back in the origianl to get their y's.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. algebra

    Find the domain and range of the function. 1. f(x)= x^2-x I got: Domain= All Real Numbers Range= All Real Numbers > -1 (with a line under the greater than sign) 2. f(x)= 1-x^2 I got: Domain= All Real Numbers Range= All Real Numbers …
  2. math

    Identify the domain and range of the following: f(x) = 4-x^2, -5<x<-1 3/2x + 3/2, -1<x<3 (both "<" signs are actually less than or equal to) x+3, 3<x<10 (x<10 is actually less than or equal to) All three are …
  3. Algebra 2

    If f(x)=3^2 g(x)= 1/6+x find the following and give the domain (f+g) (x) (3^2) + (1/6+x) x is all real numbers and x is not equal to 6 (f-g) (x) (3^2) - (1/6+x) 3^2 -6-x x is all real numbers and x is not equal to -6 (f x g) (x) I …
  4. sorry left out a "x"

    If f(x)=3^2 g(x)= 1/6+x find the following and give the domain (f+g) (x) (3x^2) + (1/6+x) x is all real numbers and x is not equal to 6 (f-g) (x) (3^2) - (1/6+x) 3^2 -6-x x is all real numbers and x is not equal to -6 (f x g) (x) I …
  5. Math

    If f(x)=3x^2 g(x)= 1/6+x find the following and give the domain (f+g) (x) (3x^2) + (1/6+x) x is all real numbers and x is not equal to 6 (f-g) (x) (3x^2) - (1/6+x) 3x^2 -6-x x is all real numbers and x is not equal to -6 (f x g) (x) …
  6. Algebra 2 Could use help asap

    I really am trying to work these problems out on my own. Please help If f(x)=3x^2 g(x)= 1/6+x find the following and give the domain (f+g) (x) (3x^2) + (1/6+x) x is all real numbers and x is not equal to 6 (f-g) (x) (3x^2) - (1/6+x) …
  7. 11th grade maths

    A.give an example of a function whose domain is {3,4,7,9}?
  8. Math Algebra 1111

    If the domain of a function F is the set of all real numbers and the domain of a function G is the set of all real numbers, under what circumstances do (F+G)(x) and (F/G)(x) have different domains?
  9. Math

    For nth root functions, I know that if "n" is even, then the domain must be equal or greater than zero. If "n" is odd, then domain will be all set of real numbers. But how do I determine the range of an n-th root function?
  10. alebra

    Let f(x)=2x^2+x-3 and g(x)=x-1. Perform the indicated operation then find the domain. (f*g)(x) a.2x^3-x^2-4x+3; domain:all real numbers b.2x^3+x^2-3x; domain: all real numbers c.2x^3+x^2+4x-3; domain: negative real numbers d.2x^3+x-3x+3; …

More Similar Questions