Function and Pic
ADDITIONAL MATHEMATICS PROJECT WORK 2012
PART 1
A family is an important institution in a society. Everyone’s hope is to have a happy family. A closely knitted family will ensure the well-being of the community and hence the nation.
Below is an example of Zulkefli and Aminah’s family tree. Answer the questions below based on the family tree given.
Diagram 1
a) Based on Diagram 1, list at least 5 different sets (Example : set of sons). b) Based on Diagram 1, draw at least three arrow diagrams to show the relation of the family. Hence, i) determine the domain, codomain, objects, images and range. ii) recognise the type of relation. iii) represent each relation above using other methods. c) Based on (b), which relation is a function? State your reason.
Part 2 a) You are required to come out with an attractive and creative card. Your card must have the following information. i) a family photo ii) a family tree b) Write a short description about your family in not more than 150 words.
Part 3
Based on Diagram 3, answer the following questions.
Diagram 3
Find
a) function [pic] and function [pic].
b) the inverse function [pic] and [pic].
c) composite function [pic], [pic], [pic] and [pic].
d) function [pic] and [pic]. Is [pic] = [pic]?
e) What can you deduce from the following composite function? [pic]and [pic] Hence, deduce the value of [pic].
Further Exploration
a) The function g is defined by [pic]. Find i) [pic], [pic], [pic], [pic], [pic] and [pic]. ii) Hence, state the function [pic] and [pic], where n is a positive integer.
b) Given the function [pic]is defined by [pic]. Find [pic]. Therefore deduce the inverse functions for the followings. Check your answers using another method. i) [pic] ii) [pic] iii) [pic]
Reflection
While you were carrying out this project,
PART 1
A family is an important institution in a society. Everyone’s hope is to have a happy family. A closely knitted family will ensure the well-being of the community and hence the nation.
Below is an example of Zulkefli and Aminah’s family tree. Answer the questions below based on the family tree given.
Diagram 1
a) Based on Diagram 1, list at least 5 different sets (Example : set of sons). b) Based on Diagram 1, draw at least three arrow diagrams to show the relation of the family. Hence, i) determine the domain, codomain, objects, images and range. ii) recognise the type of relation. iii) represent each relation above using other methods. c) Based on (b), which relation is a function? State your reason.
Part 2 a) You are required to come out with an attractive and creative card. Your card must have the following information. i) a family photo ii) a family tree b) Write a short description about your family in not more than 150 words.
Part 3
Based on Diagram 3, answer the following questions.
Diagram 3
Find
a) function [pic] and function [pic].
b) the inverse function [pic] and [pic].
c) composite function [pic], [pic], [pic] and [pic].
d) function [pic] and [pic]. Is [pic] = [pic]?
e) What can you deduce from the following composite function? [pic]and [pic] Hence, deduce the value of [pic].
Further Exploration
a) The function g is defined by [pic]. Find i) [pic], [pic], [pic], [pic], [pic] and [pic]. ii) Hence, state the function [pic] and [pic], where n is a positive integer.
b) Given the function [pic]is defined by [pic]. Find [pic]. Therefore deduce the inverse functions for the followings. Check your answers using another method. i) [pic] ii) [pic] iii) [pic]
Reflection
While you were carrying out this project,