1) The graph consists of three horizontal segments, with discontinuities (jumps) at x = 1, x = 2, and x = 3.
A horizontal segment at y = - 2 for the values x = 0 to 1.
A horizontal segment at y = - 1 for values x = 1 to 2
A horizontal segment at y = 0 for values x - 2 to 3.

2) To know whether the end points of a segment are defined by the left or the right values you have to look for the circle at the extreme of the segment: if it is a solid dot, means that the end is included, if is is an open circle (white inside) then the end is not included in that segment.

3) That function is based on the function named integer part because if relates y with the integer part of x.

The integer value function is [x] and it makes correspond y values witht he integer values of x.:

y = 0 witht the integer value of x for x between 0 and 1, excluding 1.

y = 1 with the integer value of x between 1 and 2 (excluding 2)

y = 2 with the integer value of x between 2 and 3 (excluding 3)
y = 3 with the integer value of x between 3 and 4 (excluding 4)

But our function is two units below, so it is [x] - 2

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2 years ago

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