It is a well-known fact that the idea of function plays a unifying role in the development of mathematical concepts. Yet research has shown that many students do not understand it adequately even though they have experienced a great deal of success in performing a plethora of operations on function, and on using functions to solve various types of problems. This paper will report about an assessment of the perceptions of Basotho college mathematics specialists on the notion of function. Four hundred and ninety one (491) mathematics specialists enrolled at the National University of Lesotho (Years 1 - 4) in the 2002/2003 academic year responded to the questionnaire that challenged them, amongst other things, to (a) define a function, (b) give an example of a function, and (b) distinguish between functional and non-functional situations embedded in a variety of contexts. In addition to the difficulties observed in their attempt to define a function and to provide an example of a function, results suggests that, for the majority of those who responded to the questionnaire, the idea of function seemed to be limited to common or prototypical linear and quadratic situations that could be expressed either in symbolic or graphical forms. Additionally, arbitrary correspondences and functional situations that were presented implicitly were not identified as functions by the majority of the students. This paper discusses instructional, curricular, and research implications of the findings.