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Thread: parametric equation question

  1. #1
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    parametric equation question

    Please explain how to do the following problem.
    Graph the following parametric equation. Identify the domain and range. Eliminate the parameter.
    x = sq.root of t
    y = 2 sq.root of t

    Thank you very much
    I did a table for
    t = 0, 1, 4, 9
    x = 0, 1, 2, 3
    y = 2, 1, 0, -1

    Positioned the dots (x,y), it's a line Domain (-infinity, +infinity), Range (-infinity, +infinity). When I eliminated the parameter, the equation is y=2-x
    Does it make any sense? Thank you again.
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  2. #2
    MHF Contributor
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    Hi

    Your work is OK except for the domain and range

    $\displaystyle x=\sqrt{t}$ and $\displaystyle y=2-\sqrt{t}$ are defined only for $\displaystyle t \geq 0$ which means $\displaystyle x \geq 0$ and $\displaystyle y \leq 2$

    Therefore the graph is not a complete line but a "semi-line" starting from the point (0,2)
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  3. #3
    Senior Member Pinkk's Avatar
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    The domain is not $\displaystyle (-\infty,\infty)$, and neither is the range.

    $\displaystyle x=\sqrt{t}$ is only defined when $\displaystyle t\ge 0$, which means $\displaystyle x\ge 0$, so your domain is $\displaystyle [0,\infty)$

    Likewise, $\displaystyle y=2-\sqrt{t}$ is only defined when $\displaystyle t\ge 0$, which means $\displaystyle y\le 2$, so the range of the function is $\displaystyle (-\infty,2]$.

    The equation IS $\displaystyle y=2-x$, but we must restrict the domain to $\displaystyle [0,\infty)$ because of the parameters we were initially given.
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  4. #4
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    Thank you

    running-gag and Pinkk,

    Thank you very much.
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