Shifting and reflecting functions

The  exercise appears under the Algebra II Math Mission. This exercise emphasizes recognition of translations and dilation effects on functions.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the correct stretch or compression factor: This problem provides two functions. The student is asked to determine the function that correctly represents the transformation.Sarf1.png
 * 2) Find the correct shift factor: This problem provides two functions. The student is asked to determine the function that correctly represents the transformation.Sarf2.png

Strategies
Knowledge of functional transformations and relationships between graphs are encouraged to ensure success on this exercise.
 * 1) The general function stretch and compression transformation rules are:
 * 2) f(cx) is a horizontal compression factor.
 * 3) f(x/c) is a horizontal stretch factor.
 * 4) cf(x) is a vertical stretch factor.
 * 5) f(x)/c is a vertical compression factor.
 * 6) The general function shift rules are:
 * 7) f(x-c) is a right shift and f(x+c) is a left shift.
 * 8) f(x)+c is an up shift and f(x)-c is a down shift.
 * 9) Multiplying by a negative will flip over the x-axis if it is outside of the argument and is over the y-axis if it is inside the main argument.

Real-life Applications

 * 1) Calculus describes how function change and experience with analysis of graphs will increase ability in calculus.