Function Fundamentals

Topics Description
Functions: Definitions, Notation & Terminology We learn what a function is, how it works and how to calculate the "output" value it produces when an "input" value is placed inside it. The term "mapping" is introduced as well as the terms "domain" and "range".
Curve of a Function We learn how to use a table of values to calculate the coordinates of points the function's curve passes through in order to draw its curve.
Plotting Curves with Graphical Calculator We learn how to use the Graphical Display Calculator (GDC) to plot a function's curve.
Domain & Range of a Function We learn how to find the domain and the range of a function by looking at its curve
Domain of a Function Given a function's equation, we learn how to find its domain algebraically.
Vertical Line Test How to check whether a curve represents a function \(f(x)\), simply by drawing a vertical line.
Mappings & Horizontal Line Test We define one-to-one and many-to-one mappings and learn a graphical method for checking whether a mapping is one-to-one or many-to-one mapping.
Composite Functions Given two functions \(f(x)\) and \(g(x)\) we learn how to find the expressions for the composite functions \(f\begin{pmatrix}g(x)\end{pmatrix}\) and \(g\begin{pmatrix}f(x)\end{pmatrix}\).
Inverse Functions - Part 2 Given a function \(f(x)\), we learn how to find its inverse function, \(f^{-1}(x)\), algebraically. The method is taught in detail for linear, rational and quadratic functions.

Quadratic Functions - Parabola

Topics Description IGCSE IB
Quadratic Functions - The Parabola We learn about the features of a parabola: concavity, \(y\)-intercept, axis of symmetry, vertex, \(x\)-intercepts Yes Yes
Root Factoring
Vertex Form
How to Find the Equation of a Parabola using the Vertex Form
Sketching a Parabola Without a Calculator

Transforming Functions' Curves

Topics Description
Vertical & Horizontal Translations
Vertical & Horizontal Strectches.
Reflections across the \(x\) and \(y\) axes.
Combination of Transformations
Finding Transformations

Circular Functions

Topics Description
Unit Circle: definition of \(cos(x)\) and \(sin(x)\) We define both \(cos(x)\) and \(sin(x)\) using the unit circle.
Unit Circle: definition of \(tan(x)\)
Cosine and Sine curves: \(y = cos(x)\) and \(y=sin(x)\)
The wave function: \(y=a.cos\begin{pmatrix}b(x-c)\end{pmatrix}+d\) and \(y=a.sin\begin{pmatrix}b(x-c)\end{pmatrix}+d\)