The form of the piecewise functions can be arbitrarily complex, but higher degrees of specification require considerably more user input.
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Piecewise, linear, exponential, quadratic, Onto, cubic, polynomial and absolute value.
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.
No, it is a linear transformation.
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
Linear equations are a small minority of functions.