A linear function is of the form : f(x) = ax + b (polynomial function of degree at most 1),

is there a specific term that applies for the functions of the form : f(x) = ax ?

In other words : linear functions f such that f(0) = 0.

I'm in trouble to translate from french to english...

Thanks in advance !

maybe the phrase centered on the origin?

this

or something like passes through the origin

lol... f(x) = ax is the same thing as f(x) = ax + b


except b = 0 so therefore f(x) = ax is still a linear function of the form ax + b where b = 0

did you read the op fully?
while the mathematics are the same (since mathematics is not religion) terminology varies between different countries/languages
there are eg examples in specialised fields where two languages use the same terms but the meaning is switched, so it's good to be careful when reading (higher) mathematical texts in a foreign language

if the op would have asked what the term is in german for what he is asking, it is a "homogene lineare funktion"
in some languages scientists like to be more precise than the english are

This post was edited by brmv on Mar 17 2014 10:15pm

Thanks everybody for the replies.

It's seems that, unlike in french, there is no short term in english for "homogenous linear functions".

But since "homogenous" is a little too complicated for my purpose, that will be something like what you suggested : "centered on" or "passes through" the origin.