Further Mathematics - Senior Secondary 1 - Functions

Functions

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TERM: 2ND TERM

WEEK 3
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Functions
Focus:

  • Definition of a function
  • Types of functions: One to one, Onto, Inverse, Identity, Constant, Circular functions

SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Define a function and identify its properties.
  2. Recognize the different types of functions (one-to-one, onto, inverse, identity, constant, circular).
  3. Give examples of each type of function.
  4. Understand the relationship between functions and their real-life applications.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided discussion
  • Examples and demonstrations
  • Practice exercises
  • Group work and peer sharing

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts illustrating types of functions
  • Flashcards with function types and examples
  • Worksheets for practice

 

PERIOD 1 & 2: Introduction to Functions and Definition

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of a function, explaining that it is a relationship between two sets where each input has exactly one output. Uses a real-life example, such as a vending machine, where each button corresponds to exactly one item.

Students listen attentively and ask questions to clarify their understanding.

Step 2 - Defining Functions

Defines functions formally and discusses the domain and range. Illustrates with examples on the whiteboard.

Students take notes and ask clarifying questions about domains and ranges.

Step 3 - Examples of Functions

Provides real-life examples of functions, like temperature conversions or banking transactions.

Students discuss real-life examples of functions.

Step 4 - Discussion

Teacher guides a class discussion on the importance of functions in mathematics and how they are used in various fields.

Students participate in the discussion, sharing their thoughts on the applications of functions.

NOTE ON BOARD:

  • A function is a relation from a set of inputs to a set of outputs where each input is related to exactly one output.
  • Domain: The set of possible inputs.
  • Range: The set of possible outputs.

EVALUATION (5 exercises):

  1. Define a function in your own words.
  2. What is the domain and range of the function f(x) = x²?
  3. Is the vending machine analogy a good example of a function? Why or why not?
  4. Provide a real-life situation where each input has multiple outputs. Is this still a function?
  5. If f(x) = x + 2, what is the value of f(3)?

CLASSWORK (5 questions):

  1. Define a function.
  2. What is the range of the function f(x) = x + 1?
  3. Can a person’s name be considered a function? Explain.
  4. Is f(x) = 3x a function? Why?
  5. What is the domain of the function f(x) = x² - 4?

ASSIGNMENT (5 tasks):

  1. Define and give an example of a function.
  2. Find the range of the function f(x) = 2x.
  3. Write down the domain and range for the function f(x) = √x.
  4. Provide a real-life situation where each input has only one output.
  5. Check if the relation {(-1, 3), (0, 5), (1, 6)} is a function.

 

PERIOD 3 & 4: Types of Functions

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - One-to-One Function

Introduces one-to-one functions, explaining that each output is unique for each input. Gives an example, such as f(x) = x + 1.

Students listen carefully and take notes on the characteristics of one-to-one functions.

Step 2 - Onto Function

Introduces onto functions, where every element in the range is mapped to by some element in the domain. Provides an example such as f(x) = x² (for non-negative values of x).

Students ask questions and observe examples.

Step 3 - Inverse Function

Explains inverse functions, showing that they reverse the original function. Uses an example such as f(x) = x + 3 and its inverse f⁻¹(x) = x - 3.

Students observe the process and practice examples.

Step 4 - Identity and Constant Functions

Introduces identity functions where f(x) = x, and constant functions where f(x) = c (a constant value). Demonstrates each type.

Students participate in exercises for both types of functions.

Step 5 - Circular Function

Defines circular functions (sine, cosine) in terms of angles and the unit circle.

Students take notes and attempt examples related to circular functions.

NOTE ON BOARD:

  • One-to-One Function: Each element of the range is mapped from only one element of the domain.
  • Onto Function: Every element of the range is mapped from at least one element of the domain.
  • Inverse Function: A function that reverses the original function.
  • Identity Function: f(x) = x for all values of x.
  • Constant Function: f(x) = c (a constant number) for all values of x.
  • Circular Function: Functions that relate to angles and trigonometric ratios (sin, cos).

EVALUATION (5 exercises):

  1. Determine if the function f(x) = x + 1 is one-to-one.
  2. Check if f(x) = x² is onto.
  3. Find the inverse of f(x) = x - 4.
  4. Is f(x) = 7 a constant function?
  5. Write down an example of a circular function.

CLASSWORK (5 questions):

  1. What is the definition of an onto function?
  2. Give an example of a one-to-one function.
  3. What is the inverse of f(x) = 2x + 3?
  4. Is f(x) = x³ an identity function? Why or why not?
  5. Explain the concept of a circular function with an example.

ASSIGNMENT (5 tasks):

  1. Define a one-to-one function and give an example.
  2. Find the inverse of f(x) = 3x + 5.
  3. Is the function f(x) = 4 onto? Explain.
  4. Give a real-life example of a constant function.
  5. Write down the sine function as an example of a circular function.

 

Instructional Resources:

  • Charts of different function types
  • Flashcards with examples of functions

Worksheets for practice exercises