HL AA – Functions

Function notation

Graphs of functions

Transformations

Inequalities

Odd and Even

Inverse functions

Reciprocals

1 over f(x)

Sums and Roots 1

Factor theorem

Function review

Composite functions

Graphical solutions

Modulus functions

Sums and roots 2

Remainder theorem

Traffic Light Coding for Unit

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Learning outcomes
Understanding the concept of a function.
Substitute and solve equations using algebra.
Understand the terms domain and range.
Find the inverse of a function
Understand the terms one-to-one; many-to-one; one-to-many and their applications to functions and inverses.
Graph functions with and without a GDC. Note key points on graphs (intersection with axes, maximum and minimum).
Understand and use composite functions.
Substitute and solve equations using graphs, including composite functions.
Using reciprocal graphs, including finding asymptotes from functions with and without sketches.
Solve intersection of functions using a GDC.
Transformation of functions: reflections in x and y axes; reflection in y=x line; translations; vertical and horizontal stretches.
Using the inverse function and the reflection to solve equations.
Odd and even functions
Sum and roots of a quadratic equation (alpha and beta values).
Sum and roots of all polynomial functions, where order is greater than 2.
Inequalities of functions and their graphs.
The reciprocal of a function and its graph.
The modulus of a function and its graph.
Factor theorem of polynomials.
Remainder theorem of polynomials.