IBDP Mathematics Analysis & Approaches SL Chapter 4 Notes

Rational Functions


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All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.

Even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis. The chapter discusses the following: Even and odd functions, The graph of y = [f (x)^2], Absolute value function, Rational functions and Partial fractions. The absolute value or modulus of a real number is x is its distance from 0 on the number line. Whereas partial fractions, which is later studied in calculus, is the process of decomposing a function into the sum of partial fractions so it can be integrated.
In this chapter, we look at how an object point is moved to an image point by using matrices; these are called linear transformations, which include stretches, rotations, reflections and any composition of these. Affine transformations include translation, as well. In translation, a translation vector provides the x and y components of the translation, where every point on the object moves the same distance in the same direction. Rotations about the origin through an arbitrary angle theta will be discussed to find the transformation matrix of the rotation. Stretches will look at both horizontal and vertical with scale factors of k, where the image formed is k times the distance from the y-axis. In enlargements, the scale factor k used for the enlarged image and the transformation matrix will be looked at. Composite transformations are when we apply one transformation after another.