Transformations+of+Functions

=**Transformations of Functions**=


 * __Transformation of f(x):__**


 * y = a f ( k (x -d )) + c **


 * a = vertical stretch and/or reflection of the x-axis (if negative) **
 * k = horizontal stretch and/or reflection of y-axis (if negative) **
 * d = horizontal shift **
 * c = vertical shift **


 * It is important to note that when describing and performing transformations on functions, the reflections and stretches must be done first before the shifts.**


 * __ Example 1: __**


 * y = -3 f (x +2 ) -1 **


 * This function can be described with the following:**
 * - reflection in the x-axis **
 * - vertical stretch by a factor of 3 **
 * - horizontal shift 2 left **
 * - vertical shift 1 right **


 * __ Example 2: __**


 * y = 1/2 f ( - x)**


 * This function can be described with the following: **
 * - vertical compression by a factor of 2 OR vertical stretch by a factor of 1/2 <-- (HE PREFERS THIS ONE!) **
 * - reflection in the y-axis **