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Math Help - Ordered Pairs (x, y)

  1. #1
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    Ordered Pairs (x, y)

    For questions a - b, tell whether the set of ordered pairs (x, y) defined by each equation is a function.

    (a) y = x^3 - 3x

    (b) y = + - sqrt{1 - 2x}

    (c) x + 2y^2 = 1


    How can I tell simply by looking at each equation?
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  2. #2
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    Quote Originally Posted by symmetry View Post
    For questions a - b, tell whether the set of ordered pairs (x, y) defined by each equation is a function.

    (a) y = x^3 - 3x

    (b) y = + - sqrt{1 - 2x}

    (c) x + 2y^2 = 1


    How can I tell simply by looking at each equation?
    I wouldn't look at the equation, I'd look at the graph. Do you know what the "vertical line test" is?

    Graph each function. If, when you pass a vertical line through any portion of the graph, the line intersects your function in at most one point, the graph defines a function.

    We can easily see the b and c are not functions, whereas a is.

    -Dan
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  3. #3
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    ok

    Yes, I know what the vertical and horizontal line tests are all about.

    Okay...so it is better to graph each function and apply the vertical line test to determine if it is a function.

    Thanks!
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  4. #4
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    Quote Originally Posted by symmetry View Post
    For questions a - b, tell whether the set of ordered pairs (x, y) defined by each equation is a function.

    (a) y = x^3 - 3x

    (b) y = + - sqrt{1 - 2x}

    (c) x + 2y^2 = 1

    How can I tell simply by looking at each equation?
    Is there a single y corresponding to each x where the relation is defined?
    If the answer is no its not a function.

    Thus (b) and (c) fail to be functions, while (a) does not fail this for any
    real x, so it defines a function on R to itself.

    RonL
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