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)


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


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

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.

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.

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...

Basics/composite & inverse functions 29 September 2020

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

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...

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 \(y = \ln x\))...

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,...

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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