1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sketching Regions in ℝ^2

  1. Sep 26, 2012 #1
    1. The problem statement, all variables and given/known data

    I have to sketch the following region in R^2 but i Have no idea how to do it!

    2. Relevant equations

    S1 = {(x; y) εℝ^2 : -2≤x≤4 y,≤2}

    3. The attempt at a solution

    I plotted the line from -2 to 4 on the x axis and a line greater then 2 from the y-axis but i am sure i am doing this incorrectly! any help is appreciated!
     
  2. jcsd
  3. Sep 26, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Start by plotting the equality parts: x = -2, x=4, y = 2, three straight lines. They divide the plane up into several regions. Then, examining each region, shade the ones for which x and y both satisfy the inequalities.
     
  4. Sep 26, 2012 #3
    So if i plot those points and draw the lines i get a rectangular shape on my graph is that the correct solution?
     
  5. Sep 26, 2012 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hard to say without seeing it. Describe where you have shaded.
     
  6. Sep 26, 2012 #5
    I have a graph with an x and y axis, the points drawn in and lines from each point, where the line y=2 intersects the x points i shade in the rectangular shape. If im wrong could you please tell me what to do!
     
  7. Sep 26, 2012 #6

    Mark44

    Staff: Mentor

    This is not a useful description. The region is unbounded in one direction. It is bounded on three sides by straight lines. A better description would tell us what the three boundary lines are and maybe what the points at the corners are.
     
  8. Sep 26, 2012 #7

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    -2≤x≤4. Draw two vertical lines at x= -2 and at x= 4 so that the "line from -2 to 4 on the x axis" is inside them. I don't know what you mean by "a line greater than 2 from the y-axis". y≤2 is all y less than or equal to 2 so draw a horizontal line at y= 2 crossing those two vertical lines. The region you want to shade is the area below that horizontal line and between the two vertical lines. Because there is no lower limit on y, there is no lower boundary- the region you want is the "infinite strip" between the vertical lines and below the horizontal line.
     
  9. Sep 26, 2012 #8
    Ahh thats where i was going wrong! I was using the x axis itself as a boundary! I have no idea why! Thank you for clearing that up! But in this question i have no figures.

    {(x; y) εℝ^2 : x≤y}
    Is that just the x and y axis! thank you for all your help!
     
  10. Sep 26, 2012 #9

    Mark44

    Staff: Mentor

    No. Start by graphing the line x = y. This line divides the plane into two regions. The region you want is one of them, including the boundary line.

    To determine which half plane is the right one, pick a point not on the line and see if it satisifies x ≤ y.
     
  11. Sep 26, 2012 #10
    Ah y=x will give me a 45° line through the origin?
     
  12. Sep 26, 2012 #11

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Doesn't that count as "working the problem for them"?
     
  13. Sep 26, 2012 #12
    I was in desperate need of help, I was obviously getting it horribly wrong. He just helped me out greatly and i cant thank him enough for it!
     
  14. Sep 26, 2012 #13

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, I agree with the others. I should have stopped at
    "Draw two vertical lines at x= -2 and at x= 4 so that the "line from -2 to 4 on the x axis" is inside them. I don't know what you mean by "a line greater than 2 from the y-axis". y≤2 is all y less than or equal to 2 so draw a horizontal line at y= 2 crossing those two vertical lines."

    And perhaps that is a little too much. Just noting that the lines are vertical and horizontal should have been enough.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook