# 2. Functions

The **Functions topic** includes several concepts and skills that play an important role in other parts of the course, such as: domain & range, inverse function, composite function, nature of the roots of a quadratic equation, transformations of graphs, rational functions, exponential & logarithmic functions, polynomial functions (HL), using technology to solve a variety of equations and general graphing skills.

**∼ quick link ∼**__exercise sets, quizzes & tests__ for teaching units in **Functions**

**Changes compared to previous Maths HL-SL syllabusses**:

In the previous Maths HL and Maths SL courses, only **rational functions** of the form linear/linear were considered. Now, at HL level, rational functions of the forms linear/quadratic and quadratic/linear have been added; and, also oblique asymptotes (**HL 2.13**). The other new syllabus item at HL level is the graph of \(y = {\left[ {f\left( x \right)} \right]^2}\) in **HL 2.16**.

**Functions - syllabus overview**

Syllabus item numbers are in brackets.

__SL - Functions__

**SL core (AA & AI)**

equation of a line (2.1)

concept of a function (2.2)

graphing & analysing functions (2.3, 2.4)

**SL (AA)**

composite & inverse functions (2.5)

quadratic functions & equations (2.6, 2.7)

rational functions (2.8)

exponential & logarithmic functions (2.9)

solving equations (2.10)

transformations of graphs (2.11)

__HL - Functions__

**HL (AA)**

polynomial functions (2.12)

rational functions (2.13)

inverse functions; odd & even functions (2.14)

solving inequalities (2.15, 2.16)

special graphs (2.16)

### Exercise Sets, Quizzes & Tests

AA_SL_2.2(8)_functions1_v1

Set of seven exercises (nearly all with multiple parts) covering function basics such as: identifying domain & range, composite functions, inverse functions, vertex form of a quadratic function (completing the square), graph sketching & asymptotes. Includes **worked solutions** for all exercises. Syllabus items covered go from SL 2.2* to SL 2.8.

AA_HL_Test1_functions_v1

Unit test covering following HL syllabus material: domain; range; one-to-one & many-to-one functions; composite functions; inverse function (including domain restriction); function graphing skills and use of GDC; *x*- and *y*-intercepts; vertical & horizontal asymptotes; transformations of graphs; and rational functions. Solution key (**worked solutions**) available below.

AA_HL_Test1_functions_v1_SOL_KEY

Solution key (**worked solutions**) for HL Test1 on functions above.

## Selected Pages

### Exponential & logarithmic functions 8 February 2021

go to teaching materialsSyllabus content:SL 1.7 Laws of exponents with rational exponents; laws of logarithms; change of...

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### Basics/composite & inverse functions 29 September 2020

go to teaching materials below ↴Function basics include items such as:▪ using appropriate notation for functions, composite...

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### Quadratic functions & equations 17 September 2020

There is virtually no difference between SL and HL for the syllabus content on quadratic functions & equations. All of the...

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### Inverse functions 30 April 2020

Only a one-to-one function can have an inverse function. Any one-to-one relationship (e.g. \(y = {x^3}\) or \(y = \ln x\))...

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### Other changes to a graph 30 April 2020

The graph of a function can be changed ("transformed") in ways other than the 'standard' transformations involving translations,...

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### Transformations of graphs 29 April 2020

Use the two Geogebra applet below to test your knowledge of transformations of graphs that may include a translation, reflection...

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