Objective:

To identify the basic functions of formulas and graphs.

To sketch the shift, reflection, compress, stretch, and inverse transformations of a function using demos.com

To describe features of each family of curves for each function

Introduction:

The concept of a function is a building block of many concepts of modern mathematics. It is as important in modern mathematics development as integers in arithmetic computation. We will see that many other complicated functions can be obtained through the compositions or combinations of those basic functions. Hence it is crucial to know those basic functions well. In this project, you will learn the properties of the basic functions in algebraic, graphic, and descriptive methods.

List of functions to be studied in your function library

\fFunction or Transformations Formulas Domains Ranges Original Function f (ac) = 23 (-00, 00) (-00, 00) Horizontal Shift f (ac) = (2 - 2)3 (-00, 00) (-00, 00) Vertical Shift f (ac) = (20) 3 - 3 (-00, 00) (-00, 00) Horizontal Reflection f ( ac) = (-20) 3 (-00, 00) (-00, 00) Vertical Reflection f (ac) = -203 (-00, 00 ) (-00, 00) Compression/Stretching f (ac) = (2)3 (-00, 00) (-00, 00) Inverse f (ac) = 23 (-00, 00) (-00, 00)o Square Function f (ac) = 202 (-00, 00) o Square Root Function f (ac) = Vac x 2 0 o Absolute Function f (ac) = 1201 (-00, 00) o Exponential Function f (a) = 2x (-00, 00) o Logarithmic Function f (a) = 10g2 (2) (0, -00) o Reciprocal Function f (ac) = _ (-00, 0) U (0, 0)