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Questions and Answers
Which best describes the purpose of function notation?
What is the main reason for using function notation?
When given a statement in function notation, what can you explain?
What does the term 'vertical intercept' refer to when talking about functions and their graphs?
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How can function notation help represent a relationship between two quantities efficiently?
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What are 'maximum' and 'minimum' when talking about functions and their graphs?
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What can a student do when given a graph of a function?
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How can a student explain the average rate of change of a function?
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What can a student do when given a description or visual representation of a situation?
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How can a student compare features of graphs of functions?
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What does a student understand when given an equation in function notation?
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What can a student determine when given a description of a function in a situation?
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Study Notes
Understanding Functions
- A function is a relationship between two quantities where each input corresponds to exactly one output.
- Independent variables are the inputs or values that are being manipulated, while dependent variables are the outputs or results.
Identifying Variables and Representing Functions
- Words, graphs, and function notation can be used to represent functions.
- Function notation is a concise way to express a function, using the format f(x) = output value.
Making Sense of Descriptions and Graphs
- Graphs of functions provide visual representations of relationships between variables.
- Graphs can be used to identify key features such as horizontal and vertical intercepts, maxima, and minima.
- Important features of graphs can be used to explain real-world situations.
Function Notation and Representation
- Function notation is used to efficiently represent relationships between variables.
- Statements in function notation can be used to sketch graphs of functions.
- Function notation can be used to write equations that represent the rules of functions.
Understanding Graphs and Features
- The average rate of change of a function can be estimated or calculated between two points on a graph.
- Graphs can be used to identify important features such as maxima, minima, and intercepts.
- Features of graphs can be explained in terms of real-world situations.
Sketching Graphs and Comparing Features
- Descriptions or visual representations of situations can be used to sketch graphs showing important features.
- Graphs of functions can be compared to explain how they relate to real-world situations.
Understanding Piecewise Functions
- A piecewise function is a function that is defined by multiple rules for different intervals of the domain.
- Graphs of piecewise functions can be sketched when the rules are given.
- Rules of piecewise functions can be written in function notation and explained in terms of real-world situations.
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Description
Test your knowledge on functions and graphs by answering multiple choice questions related to explaining relationships, identifying variables, interpreting descriptions and graphs, using function notation, and understanding the concept of function notation.
