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’

download: 4_Qs_function_basics_1_with_answers

accessible SL question

moderate SL / accessible HL question

discriminating SL / moderate HL question

discriminating HL question


Course planning / teaching notes:

 ♦ teaching materials

WRK_2-1-25v1_SLHL_domain_range smiley laugh
Worksheet for matching given function with graph and domain & range (answers included)

EXS_2-1-30v2_SLHL_domain_range smiley laugh
Exercise set with 9 questions on identifying domain & range of a variety of functions (answers included)

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.

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.

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)

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

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)

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

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