aidemia--modules-lessonplan_request	Titles of parts of the lesson must be formatted as headings
What to create	Lesson script
Which subject	Mathematics
What topic	Functions
What length (min)	30
What age group	Year or Grade 9
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Include images descriptions
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Lesson Script: Understanding Functions

Objective

By the end of this lesson, students will be able to:

• Define what a function is.
• Determine if a relation is a function.
• Identify and use function notation.
• Evaluate functions for given inputs.

Introduction (5 minutes)

Begin the lesson by asking students if they have encountered the term “function” before. Write down responses on the board. Explain that functions are a fundamental concept in mathematics that describe relationships between variables.

Introduce the concept with the following definition:

What is a Function?

A function is a relation that assigns exactly one output value for each input value.

Part 1: Identifying Functions (10 minutes)

1.1: Relations

Start by differentiating between a relation and a function. A relation can be any set of ordered pairs, while a function has the specific rule that every input (x-value) must map to one and only one output (y-value).

Example

• Relation: {(1, 2), (2, 3), (3, 4), (1, 5)}

  • This is not a function because the input '1' corresponds to two outputs (2 and 5).

• Function: {(1, 2), (2, 3), (3, 4)}

  • This is a function because each input has a unique output.

1.2: The Vertical Line Test

Introduce the vertical line test as a way to determine if a relation is a function. If a vertical line crosses the graph of the relation more than once, then it is not a function.

Activity

Show a set of graphs and ask students to use the vertical line test to determine whether each graph represents a function.

Part 2: Function Notation (8 minutes)

2.1: Understanding Function Notation

Introduce function notation and explain that a function can be represented using symbols. For example, ( f(x) ) represents a function ( f ) evaluated at ( x ).

Example

If ( f(x) = 2x + 3 ), then:

• ( f(1) = 2(1) + 3 = 5 )
• ( f(2) = 2(2) + 3 = 7 )

2.2: Evaluating Functions

Provide students with several function expressions and have them practice evaluating these functions for specific inputs.

Part 3: Real-World Applications (5 minutes)

Discuss real-life examples of functions:

• Banking (interest calculations)
• Physics (distance, speed, and time relationship)
• Biology (growth models)

Emphasizing how functions appear across different fields can help students understand the importance of this mathematical concept.

Conclusion (2 minutes)

Summarize the key points covered in the lesson:

• Definition of functions
• How to identify and use function notation
• Evaluating functions

Encourage students to practice these concepts to solidify their understanding.

Homework (5 minutes)

Tasks

1. Identify and classify the following relations as functions or not:

   • A: {(0, 1), (1, 2), (3, 4), (0, 3)}
   • B: {(2, 3), (3, 5), (5, 3)}

2. Use the function ( g(x) = 3x^2 - 2x + 1 ) to find:

   • ( g(0) )
   • ( g(1) )
   • ( g(2) )

3. Sketch the graph of the following function, and determine if it passes the vertical line test: ( h(x) = x^2 - 4 )

Answers

1. • A: Not a function (input 0 maps to two outputs)
   • B: A function (all inputs map to unique outputs)
2. • ( g(0) = 1 )
   • ( g(1) = 2 )
   • ( g(2) = 5 )

3. The graph of ( h(x) = x^2 - 4 ) is a parabola that opens upwards. It passes the vertical line test, so it is a function.

End of Lesson

Thank you for your participation! Be prepared to discuss your homework in the next class.