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anonymous

  • 5 years ago

can somebody explain me to draw graphs of equations like [x]+[y]=5 as fast as possible?

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  1. anonymous
    • 5 years ago
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    [x] is the box function also known as the greatest integer function..

  2. anonymous
    • 5 years ago
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    for starting ideas..i was thinking of plotting some particular points like (5,0),(0,5),(3,2),(2,3),(1,4),(4,1)..

  3. anonymous
    • 5 years ago
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    then I would probably think of the non-integers..for non-integers say in [0,1) we have [x]=0 so [y]=5 is needed which means [5,6) is the range of y..

  4. anonymous
    • 5 years ago
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    now, hence we get a rectangle with x-coordinates in [0,1) and y-coordinates in [5,6)..the whole region i.e. the whole set of points within the rectangle must be satisfying the equation..

  5. anonymous
    • 5 years ago
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    similarly for any x in [n,n+1) we get a rectangle with y in [n+5,n+6) and the points in/on the rectangle satisfy the equation...

  6. anonymous
    • 5 years ago
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    for negative x say in [-1,0), [x]=-1 so [y]=6 which means y will vary from [6,7). So for x in [n,n+1)...(n being negative)...we have y in [|n|+5,|n|+6). Lets check this: if x lies in [-2,-1) we have, [x]=-2 so [y]=7 which means y will vary from [7,8).[|-2|+5,|-2|+6)=[7,8)...

  7. anonymous
    • 5 years ago
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    So our graph is done...:) But i seek more shorter ways..any tricks,insights,ideas :)

  8. watchmath
    • 5 years ago
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    If [x]=n, i.e n<=x<n+1 then [y]=5-n. So 5-n<=y < 4-n

  9. mathteacher1729
    • 5 years ago
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    It's gonna look like the attached graph. :)

  10. anonymous
    • 5 years ago
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    can somebody explain how to factorize the equation x^4+x^3-2x^2-6ax-4a^2=0

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