Group 21 Member: Lam King Ho (98003010)

Lau Shu Fat (98003430)

Li Chi Chung (98002690)

Lam Wing Yin (98002850)

Poon Hing Sheng (98249700)

Educational Communication and Technology (EDD5161A)

PowerPoint Presentation

Topic: Concept and Graphical Representation of Functions

GO

Concept of function:

Trigonometric functionLogarithmic functionQuadratic function

Design Objectives:

Enhance students’ interest in understanding concept of functions and graphical representation of functionsProvide a time-saving package for student/teacher in drawing graphs of different functionsEnable a quick understanding of graphical variations upon changes of the coefficientsApplicable to varies level of students ( Form 3 to 5)

Guidelines to use:

Designed for students to use before or after the class but NOT in the class

Designed as assisting program besides the classroom teaching

Target Student :Age: Form two to Form fourAbility: Band 3Attitude: self-motivated, eager to learn

Authors’ part of design:

Concept of function ( Lam king ho & Poon hing sheng )Trigonometric function ( Li chi chung & Lau shu fat )Logarithmic function ( Lam wing yin & Lam king ho )Quadratic function ( Lau shu fat & Lam king ho )

Function: f(x)=x+5

x

Function: f(x)=x+5

x

Function: f(x)=x+5

Value

x= 1 6

Function: f(x)=x+5

Value=

Function: f(x)=x+5Function: f(x)=x+5Function: f(x)=x+5

x= -3 2

Function: f(x)=x+5

Value=

Function: f(x)=x+5Function: f(x)=x+5Function: f(x)=x+5

x= 4/9 49/9

Function: f(x)=x+5

Value=

Function: f(x)=x+5Function: f(x)=x+5Function: f(x)=x+5

Let f(x) = x + 5

when x = 1 ,

f(1) = 1 + 5

= 6

Let f(x) = x + 5

when x = -3,

f(-3) = -3 + 5

= 2

Let f(x) = x + 5

find f(4/9).

y

x

y = ax2 + bx + cy = ax2 + bx + c

Use this to plot the following graphs

y = x2

y = -x2

y = x2 - x - 6

y = -x2 - x - 6

y = 2x2 - x + 5

y = -2x2 - x + 5

1.

2.

3.

Then comparing their shapesThen comparing their shapes

y = ax2 + bx + c

For a > 0Curve open upwards

Eg.1

y

x

y

x

Eg.2

y = ax2 + bx + c

For a > 0Curve open upwards

y = ax2 + bx + c

For a > 0Curve open upwards

y

x

y

x

y = ax2 + bx + c

For a < 0Curve open downwards

Eg.1

y

x

y = ax2 + bx + c

For a < 0Curve open downwards

Eg.2

y

x

y = ax2 + bx + c

For a < 0Curve open downwards

y = ax2 + bx + c

For c > 0y-intercept is positive

y

x

Eg.1

y = ax2 + bx + c

For c > 0y-intercept is positive

y

x

(0, c)

Eg.2

y = ax2 + bx + c

For c > 0y-intercept is positive

y

x

(0, c)(0, c)

y

x

y = ax2 + bx + c

For c < 0y-intercept is negative

Eg.1

y

x

(0, c) y = ax2 + bx + c

For c < 0y-intercept is negative

Eg.2

y

x

(0, c)

(0, c)

y = ax2 + bx + c

For c < 0y-intercept is negative

y

x

y = ax2 + bx + c

For c = 0Eg.1

y

x

y = ax2 + bx + c

For c = 0

Eg.2

y

x

y = ax2 + bx + c

For c = 0

y

x

y = ax2 + bx + c

a > 0,c > 0

a < 0,c > 0

a < 0,c < 0

a > 0,c < 0

Click the corrected answer

y

x

y = sinx, y = cosx, y = tanxy = sinx, y = cosx, y = tanx

Use this to plot the following graphs

1. sinx

Then comparing their shapesThen comparing their shapes

2. cosx

3. tanx

1. y = sin(x)Eg.1

y

x

2. y = sin(2x)

1. y = sin(x)Eg.2

y

x

2. y = sin(2x)

y = sin(x)

1. y = sin(x)y

x

2. y = sin(2x)

y = sin(2x)

y = sin(x)

1. y = cos(x)Eg.1

y

x

2. y = cos(2x)

1. y = cos(x)Eg.2

y

x

2. y = cos(2x)

y = cos(x)

1. y = cos(x)y

x

2. y = cos(2x)y = sin(2x)

y = cos(x)

1. y = tan(x)Eg.1 y

x

2. y = tan(2x)

1. y = tan(x)Eg.2 y

x

2. y = tan(2x)

y = tan(x)

y

x

y = tan(x)

y = tan(2x)

1. y = tan(x)

2. y = tan(2x)

y

x

A , B , C

B , C , A

C , B , A

C , A , B

Match the corrected order:

A

C

B

Sin ,Cos, Tan

Meaning of Common Meaning of Common LogarithmLogarithm

Graph of y=10x

0

1

2

3

4

5

6

7

8

9

10

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0x

y

Using the graph of log y = x to find

the value of the following:

a) log 2 = ( )

Graph of y=10x

0

1

2

3

4

5

6

7

8

9

10

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0x

y

b) log 5 = ( )

c) log 10 = ( )

0.3

0.7

1

Graph of y=10x

0

1

2

3

4

5

6

7

8

9

10

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0x

y

For y = 10x

a: y = 6

b: y = 7

c: y = 8

d: y = 9

When x = 0.85, value of y is :