Topic 2 – Core: Functions and equations

Functions

1. f(x) notation

Completing the Square

1. Completing the square
2. Applications of completing the square

Polynomials

Quadratic Equations

Quadratic Equations – Roots and Discriminant

Quadratic Graphs

Algebraic Long Division

1. Algebraic long division

Factor and Remainder Theorems

Working with Functions

1. f(x) notation
2. Domain and range
3. Exam Questions - Domain and range
4. Even & Odd Functions
5. Combination of functions
6. The inverse of a function
7. Graphical relationship between f(x) and its inverse
8. Injections, surjections, bijections
9. Composition of functions and inverse functions

Modulus Functions

1. The modulus function
2. Graphing y=|f(x)|
3. Graphing y=f(|x|)
4. Exam Questions - Modulus functions graphing

Sketching Cubic and Reciprocal Curves

1. Sketching cubic curves
2. Sketching reciprocal curves of the form y = k/x
3. The graph of f=1/f(x) given the graph of y=f(x)

Graph Transformations and Asymptotes

1. Translations of graphs
2. Reflections of graphs
3. Stretches of graphs

Exponential Functions and Logarithms

1. Simplifying and expanding

The Exponential Function e^x and Natural Log Functions

1. The exponential function e^x
2. Sketching exponential graphs based on transformations
3. The natural logarithmic function, ln x

Graphs of Rational Functions

1. Improper types / oblique asymptotes
2. Relationship between the graph y=f(x) and y²=f(x)