Lecture on Transformation of Functions

Introduction

• Welcome to mathcodeserved.com
• Topic: Transformation of functions
• Focus: Vertical and horizontal shifts
• Use: Algebra 2 formulas from mathcodeserved.com

Steps for Transformation

1. Identify the family of the function
2. Determine the shifts or transformations
3. Sketch the graph of the function

Example 1: Absolute Value Function

• Function: y = |x + 2|
• Family: Absolute value (V-shaped graph)
• Transformation Formula: y = a|x - h| + k
• Transformation:
  • Write function in transformational form: y = 1|x + 2| + 0
  • Shift: 2 units left (x + 2 indicates left shift)
• Graphing: Sketch parent function with guiding points (-1, 1), (0, 0), (1, 1) and shift 2 units left

Example 2: Quadratic Function

• Function: y = x² - 4
• Family: Quadratic (U-shaped graph)
• Transformation Formula: y = a(x - h)² + k
• Transformation:
  • Write function in transformational form: y = 1(x - 0)² - 4
  • Shift: 4 units down
• Graphing: Use guiding points (-1, 1), (0, 0), (1, 1) and shift 4 units down

Example 3: Radical Function

• Function: y = √(x - 4)
• Family: Radical
• Transformation Formula: y = a√(x - h) + k
• Transformation:
  • Write function in transformational form: y = 1√(x - 4) + 0
  • Shift: 4 units to the right
• Graphing: Use guiding points (0, 0), (1, 1), (4, 2) and shift 4 units to the right

Example 4: Cubic Function

• Function: y = (x - 3)³ + 2
• Family: Cubic
• Transformation Formula: y = a(x - h)³ + k
• Transformation:
  • Write function in transformational form: y = 1(x - 3)³ + 2
  • Shifts: 3 units to the right and 2 units up
• Graphing: Use guiding points (-1, -1), (0, 0), (1, 1) and apply shifts

Conclusion

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