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Determining if polynomial function

  1. Sep 17, 2011 #1
    1. The problem statement, all variables and given/known data

    We know that a polynomial function is anything with a positive exponent and a rational number.

    a) - / x^3 -4


    d) 3x^-1 - 11

    g) y= [sqrt of term]3x^2 -5x


    2. Relevant equations



    3. The attempt at a solution

    c) 1 / x^3 - 4
    (do we use exponents to verify ?)
    i
    e) 1^1 / x^3 -4^1
    1-3 = -2 , 1-1 = 0
    Therefore there is a negetive exponent on the x^3, is that why?

    4d) y= 3^x-1 - 11
    (how do u know this isnt?)

    g) [sqrtofentireterm] 3x^3-5x

    Why is that not a polynomial function?

    Thnx 4 the help!
     
  2. jcsd
  3. Sep 17, 2011 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, we don't know that! That is wrong. A polynomial function can has the variable, x, only to positive integer exponents. The coefficients can be any numbers, not just rational numbers.

    what does the "-/" mean? Is that an attempt at a squareroot symbol? Better would be "sqrt(x^3- 4) which is the same as (x^3- 4)^(1/2). That's not a polynomial because it has a fractional exponent.

    negative exponent

    again, sqrt= exponent 1/2.

    is that 1/(x^3- 4) or (1/x^3)- 4?
    In either case, there is a negative exponent, (x^3- 4)^(-1) or x^(-3)- 4.

    I hav no clue what you are doing here.

    3^(x- 1) does not have x to a power.

    Again, because of the square root= 1/2 power.

     
  4. Sep 17, 2011 #3
    Therefore there is a negetive exponent on the x^3, is that why?

    4d) y= 3^x-1 - 11
    (how do u know this isnt?)

    3^(x- 1) does not have x to a power

    Why do you mean does not have x to a power??


    c) 1 / x^3 - 4
    (do we use exponents to verify ?)

    is that 1/(x^3- 4) or (1/x^3)- 4?
    In either case, there is a negative exponent, (x^3- 4)^(-1) or x^(-3)- 4.

    How is there a negetive exponent there... how do u verify? There is no braackets anywhere on my page so i wrote it as written. Do u evalue the exponents in the divsion and then it comes out as a negetive exponent?
     
  5. Sep 18, 2011 #4

    eumyang

    User Avatar
    Homework Helper

    Do you know the properties of exponents? Specifically, this one:
    [tex]a^{-n} = \frac{1}{a^n}, a \ne 0[/tex]
    If not, you'll need to review them.
     
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