Study objectives include identifying and analyzing the most common mistakes in finding the domain of algebraic functions committed by first-year students in the Civil Engineering program when studying the Pre-Calculus course. The study sample consisted of 25 male and female students enrolled in the first year of the Civil Engineering program, taking the Pre-Calculus course at the Middle East University in Jordan. The researcher employed a qualitative approach based on a case study, collecting data from students’ responses to open-ended mathematical questions presented to them as exercises. The study utilized the APOS Theory, consisting of four stages: Action, Processes, Objects, and Schemas, with the goal of categorizing observed errors in students’ solutions to the exercises into themes. The results revealed that the errors fell into four themes: conceptual errors, procedural errors, interpretation errors, and extrapolation errors. Most conceptual errors occurred when the domain of a function represented by a graph was expressed in terms of independent variables. Procedural errors occurred when determining the domain of an algebraic function written in algebraic notation. Interpretation errors arose when students found the domain of an algebraic function through the simplified representation of the original function (equivalent function). Extrapolation errors occurred when students used the rule \(D\left( {f + g} \right) = D\left( f \right) \cap D\left( g \right)\) to find the domain \(D\left( {f*g} \right) = D\left( f \right) \cap D\left( g \right)\) , where (*) represents any arithmetic operation. The results also indicated that the participants struggled with performing operations on sets, both closed and open intervals, as well as inequalities. The study recommended implementing strategies to reduce the observed errors and improve students’ understanding of finding the domain of algebraic functions through educational activities that involve investigating and analyzing errors through class discussions.