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Math Help - Domain and Range of the parametric equation

  1. #1
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    Domain and Range of the parametric equation

    Please check whether the following problem s solved correctly. Thank you.
    Graph the following parametric equation. Identify the domain and range. Eliminate the parameter.

    x=2+q
    y=4-2q
    Constructed a table:
    q: -2, 0, 1, 2
    x: 0, 2, 3, 4
    y: 8, 4, 2, 0

    The raph s a line. Doman: (-infnity, +infnity), Range: (-infinity, + infinity)
    After I elminated the parameter, got the equaton: y=-2x+8

    Thank you very much for your help.
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  2. #2
    Member Greengoblin's Avatar
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    You have a function f(q)=(x(q),y(q))=(2+q,4-2q) whose domain is the real numbers, and whose range is a subset (or equal to) the plane, \mathbb{R}^2.

    Since x(q)=2+q, then the range of x(q) is the real numbers, \mathbb{R}, and since y(q)=4-2q the range of y(q) is also \mathbb{R}, therefore, since the function is parametric, the range of the function is the cartesian product of these two ranges, \mathbb{R}^2.

    so the function is f:\mathbb{R}\to\mathbb{R}^2
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  3. #3
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    Talking

    Quote Originally Posted by oceanmd View Post
    Please check whether the following problem s solved correctly. Thank you.
    Graph the following parametric equation. Identify the domain and range. Eliminate the parameter.

    x=2+q
    y=4-2q
    Since x = 2 + q, then q = x - 2. Thus y = 4 - 2(x - 2) = 4 - 2x + 4 = 8 - 2x.

    This is a straight line, defined for all x and eventually "covering" all y.

    I agree with your solution.
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  4. #4
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    Thank you

    stapel,

    Thank you.
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