From the reference cited by Johanna and other googling, it appears that 'fractional linear' is the 'proper' translation of 'gebrochen linear', but I don't think that is what is meant here, since 'fractional linear' refers to a function or transformation expressed as the ratio of two linear functions. From the description in the text, it appears that the function in question is a piecewise linear function, which is a a function that is everywhere linear but discontinuous in one or more of its derivatives (in plain language, it consists of a series of linear segments with abrupt changes in value and/or slope). Perhaps 'gebrochen linear' is used in both senses in Germany, or maybe the author just used the wrong term.

Sample ref:
Piecewise Linear Functions
... Piecewise Linear Functions. ... Note that this piecewise linear function is continuous and it is in fact a function because it passes the vertical line test. ...
jwilson.coe.uga.edu/EMT668/EMAT6680.Folders/ Barron/unit/Lesson%204/4.html