Determine whether the given equation represents y as a function of x and explain how you know.

a) 16x^2-y^2=0

b) 16-lxl=4y

thank you!

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  1. a) 16x^2-y^2=0
    y^2 = 16 x^2
    y = + 4 x or y = -4x
    well y is not a unique function of x. There are two possible values of y for any old x

    b) 16-lxl=4y
    y = 4 - |x| /4
    for every value of x there is one and only one value of y

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  2. (a) 16x^2 = y^2
    not a function, since there are two values of y for almost all of the values of x.
    Fails the vertical-line test.

    (b) yes. each x has a unique |x|.

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