The logit function is
$ ln \frac{F(x)}{1-F(x)} $. According to wikipedia and the variety of materials that I have read, we can write this in linear form ($\beta_0 + \beta_1x$) for purposes of logistic regression. https://en.wikipedia.org/wiki/Logistic_regression
However, the graph of this function only looks linear between $.1<p<.9$
https://en.wikipedia.org/wiki/Logit#/media/File:Logit.svg
When the texts write this as a linear equation, are they simply approximating and assuming that p is between .1 and .9, where it is mostly linear?