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.

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