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!

Homework Help: Graph of double absolute values

  1. Sep 5, 2013 #1
    1. The problem statement, all variables and given/known data
    |x| + |y| ≤ 1
    What is the region in the plane that solves this inequality?

    2. Relevant equations

    3. The attempt at a solution
    I first tried graphing it by isolating the y variable
    |y| ≤ -|x| + 1
    Then I looked at the hint we were given, which was to assume that x and y are both positive, so I treated it as if it were written
    y ≤ -x+1
    And then constructed a graph of a line that was basically y = -x+1 with a domain of [0,3]
    But then what threw me off is that the y variable does have the absolute value bars, so there can't be negative y values in the graph, right? So now I'm thinking I just have to flip the part of the graph so that it more closely resembles y=|x-1| in the domain of [0,3]. Is that correct or am I completely missing this?
  2. jcsd
  3. Sep 5, 2013 #2


    User Avatar
    Homework Helper

    I'm not sure how can the domain be [0, 3]. Can you put any value between and including 0 & 3 in for x in |x| + |y| ≤ 1?

    What I would do is graph the four inequalities. (Yes, there are four; can you figure out what they would be? You have one of them: y ≤ -x+1.) The intersection of the four graphs would serve as the graph of |x| + |y| ≤ 1.
  4. Sep 5, 2013 #3
    I don't think I actually meant domain, that's my bad. I meant my line went from x=0 to x=3 just because of the size of my graph.

    Are the inequalities:
    x + y ≤ 1
    x - y ≤ 1
    -x + y ≤ 1
    -x - y ≤ 1
  5. Sep 6, 2013 #4


    User Avatar
    Homework Helper

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted