Can Git really track the movement of a single function from 1 file to another? If so, how?

This functionality is provided through git blame -C <file>.

The -C option drives git into trying to find matches between addition or deletion of chunks of text in the file being reviewed and the files modified in the same changesets. Additional -C -C, or -C -C -C extend the search.

Try for yourself in a test repo with git blame -C and you'll see that the block of code that you just moved is originated in the original file where it belonged to.

From the git help blame manual page:

The origin of lines is automatically followed across whole-file renames (currently there is no option to turn the rename-following off). To follow lines moved from one file to another, or to follow lines that were copied and pasted from another file, etc., see the -C and -M options.

As of Git 2.15, git diff now supports detection of moved lines with the --color-moved option. It works for moves across files.

It works, obviously, for colorized terminal output. As far as I can tell, there is no option to indicate moves in plain text patch format, but that makes sense.

For default behavior, try

git diff --color-moved

The command also takes options, which currently are no, default, plain, zebra and dimmed_zebra (Use git help diff to get the latest options and their descriptions). For example:

git diff --color-moved=zebra

As to how it is done, you can glean some understanding from this email exchange by the author of the functionality.

A bit of this functionality is in git gui blame (+ filename). It shows an annotation of the lines of a file, each indicating when it was created and when last changed. For code movement across a file, it shows the commit of the original file as a creation, and the commit where it was added to the current file as last change. Try it.

What I really would want is to give git log as some argument a line number range additionally to a file path, and then it would show the history of this code block. There is no such option, if the documentation is right. Yes, from Linus' statement I too would think such a command should be readily available.