HL Functions and Algebra

Function Notation

Relationships

Modulus

Polynomial Roots

Composite Functions

Transformations

Factor Theorem

Row Reductions

Inverse Functions

Reciprocals

Remainder Theorem

Functions Review

What do I need to know?
  • Use the function notation including: substituting into functions; solving functions, find the inverse of a function.
  • Find composite functions.
  • Understanding the terms domain and range.
  • Use the GDC to graph functions, including finding intercepts, roots, and adjusting the window.
  • To to able to sketch a graph of a function.
  • Understand and find asymptotes.
  • Understand: a one-to-one function (a function with an inverse), a many-to-one function (a function without an inverse) and a one-to many relationship (not a function).
  • Solve inequalities with and without graphs, including using a sign diagram.
  • Understand the modulus function and solve equations and inequalities with and without a GDC.
  • Transform a graph using: translations, stretches and reflections.
  • Find the graphical solution to the reciprocal of a function.
  • Understand factor and remainder theorems (not included in chapters 2 and 5).
  • Understand the difference between odd and even functions.
  • Find factors and roots for any polynomials.
  • Solve 3 simultaneous equations by use of a GDC.
  • Solve 3 simultaneous equations by use of row reduction.
How long will this unit take?

This is the real start of your HL course. This unit will take 5-7 weeks to complete and the terminology and notation will be used throughout the rest of the course. You will need a solid understanding of algebra (especially quadratics) and by the end of this unit you should have a full grasp on how to graph with your GDC. This is an important unit to master as so much notation for other topics uses functions.

Function notation

This page introduces the idea of a function, input, output and notation used.

On this page:

  • Powerpoint lesson
  • Worksheet with worked answers
  • 2 Video re-caps/questions

 

 

 

Composite Functions

This page introduces the idea of composite functions (putting one function into another).

On this page:

  • Powerpoint lesson
  • Worksheet with worked answers
  • 1 Video re-cap

 

 

 

Inverse Functions

This page shows how to find an inverse of a function.

On this page:

  • Powerpoint lesson
  • Worksheet with worked answers

 

 

 

Relationships and functions

This page will investigate the idea of a function and when functions have inverse and when a relationship is not a function.

On this page:

  • Powerpoint lesson
  • 1 video with a recap

 

 

Transformations

This page will go through how functions are translated (reflections, stretches and transformations).

On this page:

  • Powerpoint lesson
  • Worksheet with worked answers
  • 3 videos with a recap

 

 

Reciprocals of Functions

This page will go through the graphs of reciprocal functions.

On this page:

  • Powerpoint lesson
  • Worksheet with answers
  • 3 videos with a recap

 

 

Modulus Functions

This page will go through modulus functions with and without a GDC.

On this page:

  • Powerpoint lesson
  • Worksheet with answers

 

 

Remainder Theorem

Remainders of polynomials

On this page:

  • Worksheet with worked answers
  • 2 Recap videos
Factor Theorem

Factor Theorem

On this page:

  • 2 Lessons
  • Worksheet with worked answers
  • 1 Recap videos
Roots of Polynomials

This page will go through the roots of polynomials, sums and roots.

On this page:

  • Worksheet with answers

 

 

Row Reduction

Solving 3×3 simultaneous equations, unique solutions, infinite solutions, and no solutions.

On this page:

  • 2 Powerpoint lesson
  • Worksheet with worked answers
  • 3 videos with a recap