Graphing functions using transformations

Aim:

To analyse the changes in the graph of a function according to some slight changes in the definition .

Concepts:

[list=1][*]Graph of Function[/*][/list]

Discussion:

[list=1][*]If we know the graph of the function f(x) we can obtain the graphs of the functions f(x)+a and f(x+a) by translation.[/*][*]This idea helps us to imagine the graphs of some functions in the graph of the base function is known[/*][/list]

Procedure:

[list=1][*]Draw the graph of f(x)=x^2[/*][*]Create a number slider a with increment 0.1[/*][*]Draw the graph of g(x)=f(x+a) (Input f+a)[/*][*]Observe how the graph of g(x) changes according to a.[/*][/list]

Shifting of Graphs f(x)+a

Do the above observations for different functions such as

1.x^3[br] 2. x^4

Activity 1:

Procedure:

[list=1][*]Draw the graph of f(x)=x^2[/*][*]Create a number slider a with increment 0.1[/*][*]Draw the graph of g(x)=f(x+a) (Input f+a)[/*][*]Observe how the graph of g(x) changes according to a.[/*][/list]

Shifting of Graphs f(x+a)

Do the above observations for different functions such as

1.x^3[br]2.x^4

Graphing functions using transformations

Aim:

Concepts:

Discussion:

Procedure:

Shifting of Graphs f(x)+a

Do the above observations for different functions such as

Activity 1:

Procedure:

Shifting of Graphs f(x+a)

Do the above observations for different functions such as

Activity 2:

Information: Graphing functions using transformations