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How are functions and their inverses determined?
How are the basic transformations of graphing applied to the graphs of all functions?
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Student Learning Map
- Topic:Theory of Functions and their Graphs
- Subject(s):Math
- Days:12
- Grade(s):11, 12
Key Learning:
Demonstrate an understanding of the theory of functions.
Unit Essential Question(s):
Lesson Essential Question(s):How are the domain and range of functions determined? (A)How are relations between two variables determined to be functions? (A)How is function notation used to evaluate functions? (A)Lesson Essential Question(s):How are intervals where functions are increasing or decreasing determined? (A)How are relative maximum and relative minimum values of functions determined? (A)How are even and odd functions identified? (A)Lesson Essential Question(s):How can graphs of common functions be recognized? (A)How are vertical shifts, horizontal shifts, and reflections used to help sketch graphs of functions? (A)How are vertical shifts, horizontal shifts, and reflections used to help sketch graphs of functions? (ET)How are nonrigid transformations used to sketch graphs of functions? (A)Vocabulary:Relation, Function, Input, Output, Domain, Range, Vertical Line Test, Independent Variable, Dependent Variable, Implied Domain
Concept: Lesson Essential Question(s):How are operations of addition, subtraction, multiplication, and division performed with functions? (A)How is the compositions of one function with another determined? (A)How are compositions of functions used to model and solve real-life problems? (ET)Lesson Essential Question(s):How is the inverse of a function determined? (A)How is it determined if the inverse of a function is a function? (A)Lesson Essential Question(s):
Additional Info:
Ask an experienced coworker for additional reference texts and/or other materials. Textbook Ancillary Material Technology Support Program Hands-on manipulatives Kaplan Lesson Plans
Resources:
Acquisition Lesson(s):
1. How are the domain and range of functions determined?2. How are intervals where functions are increasing or decreasing determined?3. How can graphs of common functions be recognized?4. How are operations of addition, subtraction, multiplication, and division performed with functions?5. How is the inverse of a function determined?6. How are relations between two variables determined to be functions?7. How is function notation used to evaluate functions?8. How are relative maximum and relative minimum values of functions determined?9. How are even and odd functions identified?10. How are vertical shifts, horizontal shifts, and reflections used to help sketch graphs of functions?11. How are nonrigid transformations used to sketch graphs of functions?12. How is the compositions of one function with another determined?13. How is it determined if the inverse of a function is a function?Extended Thinking Lesson(s):
1. How are vertical shifts, horizontal shifts, and reflections used to help sketch graphs of functions?2. How are compositions of functions used to model and solve real-life problems?