The quality of mathematics assignments from teachers to students is one important element that determines whether learning is effective or not. To make quality math assignments requires knowledge from the teacher about content and students, who are subdomains of mathematical knowledge to teach. This knowledge needs to be developed in prospective mathematics teachers since programmed teacher education. By focusing on one of the basic concepts in mathematics, namely the concept of function, research was conducted on 25 mathematics teacher candidates. Through interactions that occur in modified focus group discussions, we want to find out how prospective teachers construct knowledge about the concept of functions and difficulties of students. The results showed that in constructing the concept of functions and difficulties of students, teacher candidates worked backward, there were gaps in changing from one representation to another and identifying that the mastery of students' prerequisite knowledge and the order of representation used by the teacher in introducing the concept of functions affected the students' difficulties when complete assignments.