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10 May, 00:02

Determine weather the function below is an even function, an odd function, or both or neither f (x) = 3/4x

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  1. 10 May, 00:09
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    Hello!

    Even functions are functions that are symmetric with respect to the y-axis. It can be proved algebraically by determining if f (-x) = f (x).

    Odd functions are functions that are symmetric with respect to the origin. It can also be proved algebraically by determining if f (-x) = - f (x).

    1. f (-x) = f (x) | Even function

    f (-x) = 3/4 (-x) = - 3/4x

    f (x) = 3/4x

    -3/4x is not equal to 3/4x

    2. f (-x) = - f (x) | Odd function

    f (-x) = 3/4 (-x) = - 3/4x

    -f (x) = - 3/4x

    -3/4x is equal to - 3/4x

    Therefore, the function, f (x) = 3/4x, is an odd function.
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