Graphing functions using transformations
Aim:
To analyse the changes in the graph of a function according to some slight changes in the definition .
Concepts:
- Graph of Function
Discussion:
- 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
Procedure:
- 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.
Shifting of Graphs f(x)+a
Do the above observations for different functions such as
1.x^3
2. x^4
Activity 1:
Procedure:
- 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.
Shifting of Graphs f(x+a)
Do the above observations for different functions such as
1.x^3
2.x^4