Portfolio Assignment - Transformations of Functions

Type I – Mathematical Investigation Assignment

This portfolio assignment will be graded using all six assessment criteria: A, B, C, D, E, and F. To produce the graphs, use WINPLOT (or any other graphing computer/calculator program that allows you to include the graphs in the text of you assignment. Make sure that all graphs are properly prepared and presented in context in your assignment.

You will be working with the functions and investigating function transformations. In any analysis and discussion of observations and generalization, please refer to the various function concepts like domain, range, intercepts, asymptotes, axis of symmetry. You may also explore the function transformation concepts further by making and justifying conjectures about transformations on composed/combined functions  i.e. f o g, f + g, fg è how do transformations combine?

Investigation:

(i)                  Given y = f(x) + a, how are the graphs of transformed? (HINT: Choose several reasonable values for a)

(ii)                Given y = f(x + a), how are the graphs of transformed? (HINT: Choose several reasonable values for a)

(iii)               Given y = af(x), how are the graphs of transformed? (HINT: Choose several reasonable positive values for a)

(iv)              Given y = f(ax), how are the graphs of transformed? (HINT: Choose several reasonable positive values for a)

(v)                Given y = -f(x), how are the graphs of transformed?

(vi)              Given y = f(-x), how are the graphs of transformed?

Conclusion:

Summarize and justify, the general transformation of y = af(bx + c) + d on the function y = f(x)