A new 12 item research questionnaire was developed specifically to assess collegiate mathematics students' concept image of domain and zeros of rational functions. The study was designed to validate Tall and Vinner's (1981) cognitive model. Support was found for the hypothesis that students' mathematical experience influences their growth, with significant group differences found among 681 students enrolled in seven different levels of collegiate mathematics classes. In addition, the participants' performances on the research questionnaire were affected strongly by the context in which a question was asked; four contexts (simplification, division, equations and functions) were used. The results of this study indicated that students form misconception(s) in learning the concepts of domain and zeros of rational functions. Student misconceptions were identified and validated. In addition, misconceptions in two areas were found to be robust. Furthermore, support was found for the hypothesis that peripheral instances of a concept are difficult to conceptualize. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]