Transformation of Functions

1) Use the graphs of common functions (8 in total) to illustrate the concepts of vertical and horizontal translations. Give one example of vertical translation and one example of horizontal translation for each of the 8 common functions studied in class. Please, show your understanding of the concepts both algebraically and geometrically.

2) Use two example for each of the following functions to illustrate the concepts of reflections (reflection in the x-axis and reflection in the y-axis): quadratic, cubic, square root and absolute value. Please, remember to show your understanding of the concepts both algebraically and geometrically.

3) Use two examples of quadratic functions to illustrate the concepts of vertical and horizontal stretching and shrinking of functions.

Especifications:

-16 algebraic and geometric demonstrations are expected to illustrate the concepts of vertical and horizontal translations: one vertical and one horizontal for each common function.

– 8 algebraic and geometric demonstrations are expected to illustrate the concepts of reflections in the x-axis and y-axis.

– 4 algebraic and geometric demonstrations are expected to illustrate the concepts of vertical and horizontal stretching and shrinking of functions: 1 vertical stretching, 1 horizontal stretching, 1 vertical shrinking and 1 horizontal shrinking.