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Thread: Odd and Even Functions

  1. #1
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    Odd and Even Functions

    Hey this is on the Barron's SAT Math IIC Book page 45

    Which of the following functions is neither odd nor even?

    a) {(1,2),(4,7), (-1,2), (0,4), (-4,7)}

    c) {(x,y):y=x^3-1}

    why is a) even or odd?

    and isn't c) odd?

    Thanks in advance
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  2. #2
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    Quote Originally Posted by fabxx View Post
    Hey this is on the Barron's SAT Math IIC Book page 45

    Which of the following functions is neither odd nor even?

    a) {(1,2),(4,7), (-1,2), (0,4), (-4,7)}

    c) {(x,y):y=x^3-1}

    why is a) even or odd?

    and isn't c) odd?

    Thanks in advance
    For a function y(x) to be even, then y(-x) = y(x), and for y(x) to be odd, then y(-x) = -y(x).

    For a), since y(-1) = y(1) = 2 and y(-4) = y(4) = 7, the function is even.

    For c), all you need is a counter-example.

    Pick two x values of the same magnitude, say -1 and 1.

    y(-1) = (-1)^3 - 1 = -1 - 1 = -2

    y(1) = 1^3 - 1 = 1 - 1 = 0.

    Since y(-x) \neq -y(x), the function can't be odd.
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  3. #3
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    But how about for a) (0,4)? The inverse isn't listed. Does this mean that the function is still even?
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