# basics/composite & inverse functions

** Quick links**:

►

__downloadable teaching materials for function basics and composite & inverse functions__

► syllabus content for the Topic:

**SL syllabus**(see syllabus section 2.1);

**HL syllabus**(see syllabus section 2.1)

Function basics include items such as:

▪ determining the domain and range of a given function

▪ determining whether a function is an even or an odd function (type of symmetry)

▪ finding coordinates of *x*- and *y-*intercepts

▪ finding equations of horizontal and vertical asymptotes of a graph

▪ analyzing and forming composite functions

▪ relationship - graphical and analytical - between a function and its inverse

▪ finding the inverse of a given function

▪ characteristics of certain basic functions - linear, quadratic, cubic, absolute value, square root, reciprocal, inverse square

One of the most basic concepts regarding functions that students need to master is understanding (visualizing) and finding the **domain and range of a function**. The GeoGebra applet below is an interactive demonstration that I use during the first lesson on functions to emphasize the importance of **visualizing domain and range** of a functon given a graph of the function.

__4 questions__ - ‘accessible’ to ‘discriminating’

__4 questions__-

download: 4_Qs_function_basics_1_with_answers

#### Course planning / teaching notes:

** ♦ teaching materials**

WRK_2-1-25v1_SLHL_domain_range

Worksheet for matching given function with graph and domain & range (answers included)

EXS_2-1-30v2_SLHL_domain_range

Exercise set with 9 questions on identifying domain & range of a variety of functions (answers included)

EXS_2-1-40v1_SLHL_function_basics

Set of 7 exercises (neary 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.

EXS_2-1-65_SLHL_inverse_functions

Set of 6 exercises (3 without GDC, and 3 with GDC). The types of functions include: square root, rational, logarithmic, exponential and quadratic. **Answers **included on second page.

Test_SL_functions_basics_v2

unit test covering following SL syllabus material: domain; range; composite functions; inverse functions; transformations of graphs; function graphing skills and use of GDC; *x*- and *y*-intercepts; vertical & horizontal asymptotes (**solution key** posted below soon)

Test_SL_functions_basics_v2_SOL_KEY **worked solutions** for all questions on Functions-Basics SL unit test (above)

Test_HL_functions_basics_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 (**solution key** below)

Test_HL_functions_basics_v1_SOL_KEY **worked solutions** for all questions on Functions-Basics HL unit test (above)