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The name given to a set of coordinates is "coordinate system".
The set of all the x-coordinate is called The Range. * * * * * Though more often, the x-coordinates are called the DOMAIN (and the y-coordinates are the RANGE).
the range
Interpolation in general is a way to determine intermediate values from a set of coordinates. Linear interpolation would be to fit a single linear function to the entire set of coordinates. Piecewise linear interpolation would then be to determine intermediate values from the set of coordinates by fitting linear functions between each set of coordinates. Connect-the-dots so to speak.
The range