IB Math Methods

Mathematical Investigation (Type I)

 

The purpose of this assignment is to investigate the behavior of the trigonometric function : F(x)= A Sin B(X+C) +D and the transformations it undergoes  for different values of A,B,C,D

 

1. For A>0 , how does the graph of F(X)= Sin X compare with the graph of

      F(X)=A Sin(X)

 

2. For A<0 , how does the graph of F(X)= Sin X compare with the graph of

      F(X)=A Sin(X)

 

3. For B>0, how does the graph of F(X)=Sin X compare with the graph of

F(X)=Sin (BX)

 

4. For B<0, how does the graph of F(X)=Sin X compare with the graph of

F(X)=Sin (BX)

 

5. For C>0, how does the graph of F(X)=Sin X compare with the graph of

      F(X)= Sin (X+C)

 

6. For C<0, how does the graph of F(X)=Sin X compare with the graph of

      F(X)= Sin (X+C)

 

7. For D>0, how does the graph of F(X)= Sin X compare with the graph of

F(X)= Sin (X )  +  D

 

8. For D<0, how does the graph of F(X)= Sin X compare with the graph of

F(X)= Sin (X )  +  D

 

9. Given F(X) = Sin X,  find another Cosine function that has the same graph.  Explain why they are the same.

 

10. Generalize your findings to other types of functions.  Do the Tangent and Cosine functions behave in the same manner? What changes, if any, did you observe?

 

Things to keep in mind:

 

-         Use Mathematical terms and notation consistently throughout project.

-         Do not over explain.  Be precise and to the point.

-         Include two functions per graph (The basic function and the transformation)

-         As you explain the transformations, try to explain “What has changed” as well as “What has not changed”