Unit 2 - Functions
Statement of Inquiry
Models are depictions of real-life events using expressions, equations or graphs while a function is defined as a relation or expression involving one or more variables. Creating different representations of functions to model the relationships between variables, visually and symbolically as graphs, equations and tables represents different ways to communicate mathematical ideas.
Concepts
Relationships,
Representation
Relationships: the connections and associations between properties, objects, people, and ideas -- including the human community's connections with the world in which we live. READ MORE >
Representation: The manner in which something is presented.
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Learning Topics
Course Syllabus Topics
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Functions
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Mapping diagrams
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Inputs and outputs
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Domain and range
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Composite functions
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Inverse functions
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Identity functions and
one-to-one functions -
Self-inverses
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Variables
Conceptual Understandings
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Different representations of functions, symbolically and visually as graphs, equations and tables provide different ways to communicate mathematical relationships.
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The parameters in a function or equation correspond to geometrical features of a graph and can represent physical quantities in spatial dimensions.
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Moving between different forms to represent functions allows for deeper understanding and provides different approaches to problem solving
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Our spatial frame of reference affects the visible part of a function and by changing this "window" can show more or less of the function to best suit our needs.
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Functions represent mappings that assign to each value of the independent variable (input) one and only one dependent variable (output).
Further Conceptual Understandings
Unit Discussion
Questions & Suggestions
Click on the microphone icon to enter our Unit and Lesson Discussion.
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Begin a discussion thread by adding a specific question under a Lesson heading.
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Suggest links to videos and websites that have helped you in your learning.
Link to the Course Calendar
Lesson 1:
Functional Notation
and Graphing
In SeeSaw, respond to one. Then, comment to someone else with agreements/disagreements.
TOK Reflections:
What is the relationship between real life
problems and mathematical models?
Reflect
Lesson 2:
Domain and Range
Video Lesson 1
Video Lesson 2
+ Video Notes Page
Optional: Extra Practice
Ask your questions
in our Unit Discussion.
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Learn
In SeeSaw, respond to one. Then, comment to someone else with agreements/disagreements.
TOK Reflections:
In math, there are different words for the same thing; ie: trapezium vs trapezoid, surd vs root. Sometimes, different symbols are used, such as interval notation vs set notation. To what extent does the language we use shape the way that we think?
Reflect
Lesson 3:
Composite and
Inverse Functions
In SeeSaw, respond to one. Then, comment to someone else with agreements/disagreements.
TOK Reflections:
"The object of mathematical rigor is to sanction and legitimize the conquests of intuition." Jacques Hadamard What do you think?
Is the study of a function's graph as rigorous as studying the function algebraically?
Reflect
Lesson 4:
More on Functions
+ Unit Review
In SeeSaw, respond to one. Then, comment to someone else with agreements/disagreements.
TOK Reflections:
Is mathematics independent of culture?
Do you think that mathematics is just the manipulation of symbols under a set of rules?