1.1 Algebra 2 (1)

Lesson 1.1: Parent Functions and Transformations

Page 1: Introduction

• Title: Parent Functions and Transformations

• Source: ©Big Ideas Learning, LLC

• Focus: Understand various parent functions and their transformations.

Page 2: Warm-Up Activity

• Task: Plot the following ordered pairs in a coordinate plane and connect with a line.

  • Table values:

    • x: -2, 0, 3, 0

    • y: -5, -3, 3, 0

  • x: -4, -2, 0, 5

    • y: 1, -2, 3, 0

Page 3: Learning Targets

• Learning Target: Graph and describe transformations of functions.

• Success Criteria:

  • Identify function families.

  • Graph transformations of functions.

  • Explain effects of translations, reflections, stretches, and shrinks on function graphs.

Page 4: Identifying Basic Parent Functions

• Activity: Classify six graphs based on the function type.

• Types include: constant, linear, absolute value, quadratic, square root, exponential.

• Discussion Points:

  • How domain and range assist in identifying function graphs.

Page 5: Grouping Parent Functions

• Activity: Sort identified parent functions and characterize them based on graphs.

• Explanation of sorting process should be provided.

Page 6: Key Vocabulary

• Key Terms:

  • Parent Function: Basic form of a function family.

  • Transformation: Changes in size, position, or orientation of a graph.

  • Types of functions: Constant, Linear, Absolute Value, Quadratic.

• Parent Functions Table:

  Function Type	Function Rule	Domain	Range
  Constant	f(x) = 1	All real numbers	y = 1
  Linear	f(x) = x	All real numbers	All real numbers
  Absolute Value	f(x) =	x
  Quadratic	f(x) = x²	All real numbers	y ≥ 0

Page 7: Identifying Function Family Example

• Example:

  • Identify function family of graph f (V-shaped) as absolute value function.

  • Compare graphs and identify transformations: vertical shift and narrowing effect.

Page 9: Describing Transformations

• Definition: Transformation modifies the graph's size, shape, position, or orientation.

• Translation: Shift without altering the graph's features.

Page 10: Graphing Translations Example

• Example:

  • Graph g(x) = x - 4.

  • Transformation: vertical translation of 4 units down from parent function.

Page 11: Reflections

• Definition: Flipping a graph over a specified line.

• Properties of Reflections:

  • Reflected points maintain the same distance to the line of reflection.

Page 12: Graphing Reflections Example

• Example:

  • Graph p(x) = -x² will show a reflection over the x-axis of the quadratic parent function.

Page 15: Stretches and Shrinks

• Vertical Stretch: When multiplying y-coordinates by a factor > 1.

• Vertical Shrink: When multiplying y-coordinates by a factor between 0 and 1.

• Visualizations: Imagine pulling or pushing points towards/away from x-axis.

Page 19: Combinations of Transformations

• Understanding how multiple transformations affect the graph of a function is vital.

Page 20: Complex Transformations Example

• Example:

  • Graph g(x) = -|x + 5| - 3 shows a reflection in the x-axis, translation 5 units left and 3 units down.

Page 21: Modeling Real Life Example

• Using function modeling for real-life scenarios, like tracking height in physics.

• Table of Height Data:

  Time (s)	Height (ft)
  0	8
  0.5	20
  1	24
  1.5	20
  2	8

Page 23: Further Graphing Practice

• Tasks to graph various functions and identify transformations.

• Example roles of functions have been given to complete.

Page 24: Additional Application Example

• Chaining Function Values:

  • Explore the relationship of decreasing fuel values over time.

  • Use the function’s type for predictions.

Page 25: In-Class Practice

• Mini-Assessment:

  1. Identify function family of f(x) = -x + 2.

  2. Identify function family of f(x) = x² - 2.

  • Use technology for subsequent graph tasks and describe transformations.