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maths question

  • 11-04-2013 02:06PM
    #1
    Scubasteve123
    Registered Users, Registered Users 2 Posts: 8 ✭


    I should now all this stuff but i dont.. would really appreciate sum help!

    Consider the function f(x) = (2x^2 + 1)/(x^2 - 1)

    a) what is the domain of the function
    b)find the x-intercepts and the y-intercepts, if any.
    c)find all the vertical asymtotes of f, if any.
    d) find all the horizontal asymtotes of f, if any
    e) find all critical points of f, and determine in each case wether the point represents a maximum, minimum or neither
    f) use all the above information to produce a sketch of the function f.


Comments

  • #2
    Ficheall
    Registered Users, Registered Users 2, Paid Member Posts: 9,056 ✭✭✭Ficheall


    Scubasteve123 wrote: »
    I should now all this stuff but i dont.. would really appreciate sum help!

    Consider the function f(x) = (2x^2 + 1)/(x^2 - 1)

    a) what is the domain of the function
    b)find the x-intercepts and the y-intercepts, if any.
    c)find all the vertical asymtotes of f, if any.
    d) find all the horizontal asymtotes of f, if any
    e) find all critical points of f, and determine in each case wether the point represents a maximum, minimum or neither
    f) use all the above information to produce a sketch of the function f.

    a) The domain is the set of vales for which the function is defined.
    b) Let 'y' (or f(x) in your case) = 0 and solve for x to find the x-intercepts. Let x = 0 aand solve for f(x) to find the y-intercepts.
    c+d) Asymptotes are where the function is undefined with the value stretching off towards infinity, ie. trying to divide by 0.
    e) Differentiate once and solve for 0 to find critical points and the differentiate again using the sign to determine if max or min.

    Most answers to your questions are available at wikipedia.org/wiki or google.com .


  • #3
    Scubasteve123
    Registered Users, Registered Users 2 Posts: 8 ✭Scubasteve123


    ive been working on it...
    a) (-infinity, -1)
    (-1,1)
    (1, infinity) is this right by any chance...just so im 100%
    b) y intercepts is (0,-1) if im right.... and x intercepts is (?,0)..im not sure about that 1
    c)vertical asymptotes => x=1 and x=-1
    d)horizontal asymptotes => y=2
    e) the critical point is 2 and i think its a max
    f) and the graph goes up and down!

    would u be able to clearify if im write?


  • #4
    jca
    Closed Accounts Posts: 8,539 ✭✭✭jca


    Know, some.


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