National Junior College Mathematics Department 2010 2010 / SH1 / H2 Maths / Functions Page 1 of 43 National Junior College 2010 H2 Mathematics (Senior High 1) Functions (Lecture Notes) Topic 6: Functions Objectives: At the end of this topic, students should be able to understand that a function is a rule or relationship where for every input there is only one output, and that two functions having the same rule are different if they have different domains. use the function notations. use the vertical line test on a graph to determine whether it represents a function. determine the range of a function from its graph. understand the definition of a one-one function and i dentify it using a horizontal line test. explain the condition for a function to have an inverse function. obtain the inverse of a one-one function and state its domain a nd range. illustrate in graphical terms the relation between a one-one function and its i nverse. restrict the domain of a function so that the inverse exists. understand that a composite function gf is a composition of two functions, f f ollowed by g. determine if the composition of two functions exists and obtain the composite function if it exists. determine the domain and range of a composite function. recognise through examples that composition of functions is not c ommutative. §1 Set Notations The symbol ‘∈’ represents ‘belongs to’ or ‘is an element of’. For example, ‘ x ∈ » ’ means x belongs to the set of real numbers. » + represents the set of positive real numbers. It does not include zero. » − represents the set of negative real numbers. It does not include zero. { } 0 + ∪ » represents the set of non-negative real numbers.
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 1/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 2/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 3/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 4/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 5/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 6/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 7/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 8/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 9/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 10/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 11/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 12/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 13/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 14/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 15/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 16/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 17/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 18/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 19/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 20/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 21/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 22/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 23/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 24/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 25/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 26/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 27/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 28/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 29/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 30/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 31/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 32/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 33/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 34/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 35/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 36/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 37/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 38/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 39/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 40/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 41/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 42/43
7/30/2019 NJC Functions Lecture Notes Teachers Edition with Tutorial and Answers
http://slidepdf.com/reader/full/njc-functions-lecture-notes-teachers-edition-with-tutorial-and-answers 43/43
Related Documents
