Breakpoint

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A point where some property of a function changes, such as its slope. For example, a piece-wise linear, univariate function with LaTeX: k breakpoints has the form:

LaTeX: 
f(x) = a_i x + b_i \mbox{ for } c_i \le x < c_{i+1}
where LaTeX: i=1, ...,k and LaTeX: c_{k+1} is defined to be infinity and LaTeX: c_1 is the least value of LaTeX: x. This function is continuous if it is equal at breakpoints, but the slope changes if LaTeX: a_i \neq a_{i+1} for LaTeX: i=1, ..., k-1.


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