<![CDATA[This research aims to analyze students' conceptual understanding of relation and function material based on APOS theory in terms of mathematical ability. The subject of research are threestudents. The instruments used were tests of mathematics ability, tests of conceptual understanding in the relation and function material based on APOS theory, and interview. The result of the research showed that: (1) Students with high mathematical ability understand the concept of relation and function materialby performing operations algebraically (action), sketching graphs; observed function as an input-output machine; and explain the definition of function (process), explained the relationships between relation and function; understand the unique properties of function (object), and apply concepts (schema). (2) Students with average mathematical ability understand the concepts of relation and function material by performing operations algebraically (action), sketching graphs; observed function as an input-output machine; and explained the function definition (process),and understand the unique properties of function (object). (3) Students with low mathematical ability understand the concept of relation and functionmaterial by performing operations algebraically (action), sketching graphs, and observed function as aninput-output machine (process).]]>
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