Algebra

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Confused Please Help! Thanks!

Let f(x) = 1 – 3x^2. Which of the following is true? Give a brief explanation.

A. f is an odd function
B. f is an even function
C. f is neither odd nor even
D. f is both odd and even

  • Algebra -

    What are the choices?

  • Algebra -

    A. f is an odd function
    B. f is an even function
    C. f is neither odd nor even
    D.f is both odd and even


    Totally confused and would appreciate some insight. Thanks!

  • Algebra -

    an even function is one where f(x) = f(-x), that is, using either a positive number as input to the function you get the same result as if you used the opposite of that number

    and odd function is where f(x) = -f(x)

    so what if you tried f(5) and f(-5)
    f(5) = 1 - 3(5)^2 = 1 - 75 = -74
    f(-5) = 1 - 3(-5)^2 = 1 - 75 = -74

    will that be true for all ± x's ?

    mmmhhh?

  • Algebra -

    another way to look at it:

    an even function results in a reflection in the y-axis

    an odd function results in a reflection in the origin.

  • Algebra -

    So I would say that the answer would be that f can be both odd and even then. Am I correct?

  • Algebra -

    NO, no, no

    it is EVEN.

    Just make a quick sketch of the graph.
    Did you not read my explanations ?

  • Algebra -

    Yes I read them, but misinterpreted them I suppose.

    So this is an even function because x is being represented rather than y and this would be an even function resulting in a reflection in the y-axis?

    I will sketch it out.

  • Algebra -

    If this was a -f(x) then it would be odd? I think I understand now..Am I correct?

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