## Emphasis

With limited space, choices have had to be made around the scope and depth of treatment of the many topics in the courses that lead to tertiary mathematics studies.

To this end, we have made it a priority to spend more time and space exploring the fundamental thinking and the logical development of the mathematical results. We have spent less time in the more straightforward concepts and less time on material that is being progressively absorbed by modern technology.

One noteworthy inclusion however is Whetstone 38, which deals with the sketching of

To this end, we have made it a priority to spend more time and space exploring the fundamental thinking and the logical development of the mathematical results. We have spent less time in the more straightforward concepts and less time on material that is being progressively absorbed by modern technology.

One noteworthy inclusion however is Whetstone 38, which deals with the sketching of

*rational functions*– functions of the formwhere

This general class of functions includes polynomials, by making

Given that computer graphing packages such as

*P(x)*and*Q(x)*are polynomials with*Q(x)*not equal to zero.This general class of functions includes polynomials, by making

*Q(x)*the degree zero or constant polynomial, and all algebraic fractions formed by polynomials. The real roots of these functions, if there are any, are determined by putting*P(x)=0*and the points of discontinuity, if there are any, are determined by putting*Q(x)=0*. The relative sizes of the degrees of*P(x)*and*Q(x)*provide the clue to the functions’ asymptotic behaviors – the approach of a function to some line or curve.Given that computer graphing packages such as

*Autograph*now provide powerful opportunities for students to examine sketches of functions, it is our belief that it is worth paying attention to this class of functions as a way of enhancing students’ understandings.