# 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