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    Can someone help me with this functions question.

    1. Which of the following relations are both odd and even?
    I. x2 + y2 = 1
    II. x2 - y2 = 0
    III. x + y = 0
    A. only III
    B. only I and II
    C. only I and III
    D. only II and III
    E. I, II, and III

    Surely the answer is E as a function must be odd or even. But the answer is B can someone help explain?

    2. Which of the following functions is neither odd nor even?
    A. {(1,2),(4,7),(-1,2),(0,4),(-4,7)}
    B. {(1,2),(4,7),(-1,-2),(0,0),(-4,-7)}
    C. y = x3 - 1
    D. y = x2 - 1
    E. f(x) = -x

    I just dont get this one

    Thanks!
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    (Original post by Hgdfu)
    Surely the answer is E as a function must be odd or even. But the answer is B can someone help explain?
    A function can be neither if it doesn't satisfy f(-x) = f(x) nor f(-x) = -f(x). (though as atsruser says below, these (I and II) are not functions, but this is an important note nonetheless) On the topic of the question, look at the exponents of the x and y terms, and it should become clearer.
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    (Original post by Hgdfu)
    Can someone help me with this functions question.

    1. Which of the following relations are both odd and even?
    I. x2 + y2 = 1
    II. x2 - y2 = 0
    III. x + y = 0
    A. only III
    B. only I and II
    C. only I and III
    D. only II and III
    E. I, II, and III

    Surely the answer is E as a function must be odd or even. But the answer is B can someone help explain?
    Note that the question has given you a list of relations, and you are talking about functions. All functions are relations, but some relations are not functions, and thus need not map a single element to a single element.

    2. Which of the following functions is neither odd nor even?
    A. {(1,2),(4,7),(-1,2),(0,4),(-4,7)}
    B. {(1,2),(4,7),(-1,-2),(0,0),(-4,-7)}
    C. y = x3 - 1
    D. y = x2 - 1
    E. f(x) = -x

    I just dont get this one
    Have you tried plotting these functions? It will probably then become clear.
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    for a relation to be both odd and even the graph must have reflection symmetry in the y axis and also rotation symmetry about the origin.
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    Thank you so much, that has really helped!
    (Original post by the bear)
    for a relation to be both odd and even the graph must have reflection symmetry in the y axis and also rotation symmetry about the origin.
 
 
 
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