Sketching graphs

The question states:

Suppose we define {x} to be the distance from x to the nearest integer.

(a) Sketch the graph f(x) = {x}
(b) Sketch the graph of g(x) = {2x}
(c) Sketch the graph of h(x) = {x} + 1/2{2x}
(d) Sketch the graph of all points (x,y) which satisfy {x} + {y} = 1
(e) Sketch the graph of all points (x,y) which satisfy |x| + |y| = 1

For (a), does the graph look like a series of repeated triangles on the x-axis? (b) and (c) are similar to (a).

And I can't figure out (d) and (e)... hints/insights would be great. Thanks in advance!

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Originally Posted by skeeterrr

The question states:

Suppose we define {x} to be the distance from x to the nearest integer.

(a) Sketch the graph f(x) = {x}
(b) Sketch the graph of g(x) = {2x}
(c) Sketch the graph of h(x) = {x} + 1/2{2x}
(d) Sketch the graph of all points (x,y) which satisfy {x} + {y} = 1
(e) Sketch the graph of all points (x,y) which satisfy |x| + |y| = 1

For (a), does the graph look like a series of repeated triangles on the x-axis? (b) and (c) are similar to (a).

And I can't figure out (d) and (e)... hints/insights would be great. Thanks in advance!

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Attached find a graph of the greatest integer function. For this problem I would suggest making a table with a few numbers and plotting the points. The graph should become obvious quickly.

Good luck!

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Attached find a graph of the greatest integer function.

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Which software did you use to create the attached graph?

That looks a bit like Maple 13, but I may be wrong.