Functions

In this topic, we will look at

  • Composite and Inverse Functions
  • Quadratic Functions and the Discriminant
  • Rational Functions
  • Transforming Functions
  • The Factor and Remainder Theorem
  • Sums and Products of Polynomial Equations


  • Functions - The Basics

    In this page, we will look at the different types of relations including functions. The first step to gaining a good understanding of functions, is to think about inputs and outputs. Once that is clear, you should be able to deal with domain and range, as

  • Quadratics

    On this page we will look at quadratic expressions and how the different factorised forms link to the shape of the graph. We will also get an understanding about how the discriminant affects not only the number of roots of a quadratic equation, but also ho

  • Rational Functions SL

    On this page, we will look at the properties of the reciprocal function and the rational function. You may be required to draw a sketch of these functions. In these cases, it is important to know how to find the vertical asymptote, the horizontal asymptote

  • Transforming Functions SL

    For the topic of transforming functions, we need to understand the effect of translating, reflecting and stretching has on functions. You may be asked to describe the transformations, sketch graphs or find the coordinates of points that have been transform

  • Transforming Functions HL

    For the topic of transforming functions, we need to understand the effect of translating, reflecting and stretching has on functions. You may be asked to describe the transformations, sketch graphs or find the coordinates of points that have been transform

  • Factor and Remainder Theorem

    The factor theorem is a special case of the remainder theorem, in that (x-a) is a factor if and only if P(a)=0

  • Sums and Products of Roots

    On this page, we learn all about roots of polynomial equations and how to use the formulae for the sum of the roots and the product of the roots.