NJC 03_2016_-_2017_H2_Maths_Functions_Lecture_Questions_(Stu)_(Final)

National Junior College Mathematics Department 2016 Functions Page 1 of 12 National Junior College 2016 – 2017 H2 Mathematics Functions Lecture Questions Part 1. Key Questions to answer:  What are the set builder and interval notations, and how do you use them? Prerequisite knowledge: Number Line, Set Notation and Language Lecture Readings: Section 1 Question 1.1 What do the following symbols represent? , , , , ,    Answer: : set of integers, : set of positive int egers, : set of negative integers, : set of real numbers, : set of positive real numbers, : set of negative real numb ers   Question 1.2 What are set operators and how are they used as an extension to the above sets? Question 1.3 How do we use the set builder notation or the interval notation to represent a set of values? Range of Values Representation as a Set Set Builder Notation Interval Notation 23 x    | 2 3xx    ( 2, 3) 23 x    | 2 3xx    [ 2, 3) 23 x   2x  |2xx  ( , 2]  3x Question 1.4 What is the difference between the use of round and square brackets in the interval notation? Part 2. Key Questions to answer:  What are relations and functions?  How do you determine graphically whether a relation is a function?  How do you define and represent a relation/function? Prerequisite knowledge: Curve Sketching Lecture Readings: Section 2

National Junior College Mathematics Department 2016 Functions Page 2 of 12 Question 2.1 (Numerical representation of relations or functions) Which of the following relations is a function? Function Not a Function Function Question 2.2 (Diagrammatical representation of relations or functions) Which of the following relations is a function? Learning Point(s): (a) A relation is an association between 2 sets of data (in our case, they are usually numbers). (b) A function is a relation that has exactly one output for every possible input [colloquially we think of it as many-to-one (function) versus one-to-many (not a function)]. Question 2.3 (Algebraic representation of relations or functions) Which of the following relations is a function? h : , {0, 4},x x x g : , { 4, 0},x x x  f : , {0, 4},x x x  p( ) .xx  The relations g and h are not functions. Why?  The relation f is a function. Note that  f xx is known as the rule of function f. {0, 4} is the domain (“inputs”) of f, denoted by fD . {0, 2} is the range (“outputs”) of f, denoted by fR . A function is defined by both its rule and domain.  If the domain of a function is not given explicitly, the convention is that the domain is the set of all numbers for which the rule makes sense and defines a real number. In the case of function p, the domain of p is [0, ). The corresponding range of p is [0, )pR  .  Functions p and f