Page 2: Advanced Transformation Examples

This page delves deeper into complex transformations using various parent functions, particularly focusing on cubic and root functions.

Example: f(x) = 4(x + 2)³-5 shows multiple transformations applied to a cubic function:

• Left shift by 2 units
• Downward shift by 5 units
• Vertical stretch by factor of 4

Highlight: The transformation of f(x) = -√(2x+6) demonstrates:

• Reflection over x-axis
• Horizontal shrink by factor of 2
• Upward shift by 6 units

Definition: Domain and range are affected by transformations, but the basic shape of the parent function remains consistent.

Vocabulary:

• Parent Function: The basic function before any transformations
• ROXA: A method for analyzing transformations in sequence

Page 1: Introduction to Function Transformations

This page introduces fundamental concepts of function transformations and their applications through practical examples. The content focuses on understanding how different transformations affect parent functions.

Definition: Function transformations are operations that modify a parent function to create new functions through shifts, stretches, and reflections.

Example: f(x) = |x-4| demonstrates a horizontal shift of the absolute value function.

Vocabulary:

• Vertical stretch/shrink: When |a| > 1 or 0 < |a| < 1
• Horizontal stretch/shrink: When 0 < b < 1 or b > 1
• Translation: Movement of a function horizontally or vertically

Highlight: The general form for function transformation is ±a f(-b(x - h)) + k, where:

• ±a affects vertical stretch/reflection
• b affects horizontal stretch/shrink
• h affects horizontal shift
• k affects vertical shift