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Math Help - Assistance with sketching relations

  1. #1
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    Assistance with sketching relations

    The question:

    Sketch the set of points (x, y) which satisfy the following relations:

    0 <= y <= 2x and 0 <= x <=2

    I have no idea where to start. Is there a way to simultaneously equate them? Is the process supposed to be intuitive? I can't get my head around it.

    Any guidance would be greatly appreciated.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Glitch View Post
    The question:

    Sketch the set of points (x, y) which satisfy the following relations:

    0 <= y <= 2x and 0 <= x <=2

    I have no idea where to start. Is there a way to simultaneously equate them? Is the process supposed to be intuitive? I can't get my head around it.

    Any guidance would be greatly appreciated.
    Hi Glitch,

    If x (domain) is between 0 and 2, inclusive,
    then y (range) is between 0 and 4, inclusive.

    Sketch 0 to 2 on the x-axis, and 0 to 4 on the y-axis.

    Complete the rectangle with corners at (0, 0), (0, 4), (2, 4), (2, 0).

    All the points inside the rectangle, including the corners and edges, satisfy the given conditions.
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  3. #3
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    Thanks for the reply.

    So when determining the range, how did you know it was between 0 and 4 inclusive? Did you substitute the upper bound of x?
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by Glitch View Post
    Thanks for the reply.

    So when determining the range, how did you know it was between 0 and 4 inclusive? Did you substitute the upper bound of x?
    Yes, I did.
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  5. #5
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    Hello, Glitch!

    Sketch the set of points (x, y) which satisfy: . \begin{array}{ccccc}0 & \leq &  y & \le &2x \\ 0 & \le &x & \le &2 \end{array}

    0 \:\le\: y \:\le\:2x means y is between the lines: . \begin{Bmatrix}y &=& 2x \\ y &=& 0 \end{Bmatrix}

    The graph looks like this:

    Code:
          |
          |               *:::::
          |             *::::::
          |           *:::::::::
          |         *::::::::::
          |       *:::::::::::::
          |     *::::::::::::::
          |   *:::::::::::::::::
          | *::::::::::::::::::::
      - - * - - - - - - - - - - - -
          0


    0\:\le\: x \:\le\:2 means x is between the lines: . \begin{Bmatrix}x &=&2 \\ x &=& 0\end{Bmatrix}


    Code:
          |
          |:::::::::|
          |:::::::::|
          |:::::::::|
          |:::::::::|
          |:::::::::|
          |:::::::::|
      - - * - - - - + - - - - - - -
          0         2


    The region satisfying both inequalities is the area shaded twice.


    Code:
          | 
          |         *
          |       *:|
          |     *:::|
          |   *:::::|
          | *:::::::|
      - - * - - - - + - - -
          0         2
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