The students in my country are supposed to be able to work with and answer questions about functions at the age of around 15. This is asserted in the standard mathematics curriculum for middle school students.
Personally, I think the definition of a function is extremely abstract and technical. Of course, I understand its importance in higher mathematics, but we are not only preparing kids to become mathematicians. Additionally, the definition of a function is rather cumbersome, and I have trouble stating it clearly at any level.
I question why we put so much emphasis on the concept of a "function" while we could be broadening our scope a bit to all relations between variables. As an example, the equation of a circle does not fall directly under the "function" category. Why does the term "function" even need to be taught to most children?
Most of the text books only deal with linear functions, quadratic functions, and 1/x.
Why should or shouldn't we teach functions to 15 year olds?