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:
Identify function family of f(x) = -x + 2.
Identify function family of f(x) = x² - 2.
Use technology for subsequent graph tasks and describe transformations.