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# HL Functions and Algebra

##### 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