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Questions and Answers
What is a relation?
What is a relation?
- A number
- A set of ordered pairs (correct)
- An equation
- An operation
What does mapping illustrate in a relation?
What does mapping illustrate in a relation?
How each element of the domain is paired with an element in the range
What is the range in a relation?
What is the range in a relation?
The set of y-coordinates
What is the domain in a relation?
What is the domain in a relation?
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What is the independent variable in a relation?
What is the independent variable in a relation?
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What is the dependent variable in a relation?
What is the dependent variable in a relation?
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What defines a function?
What defines a function?
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What is a discrete function?
What is a discrete function?
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What are continuous functions?
What are continuous functions?
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What is the vertical line test used for?
What is the vertical line test used for?
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What is function notation?
What is function notation?
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What is a variable in algebra?
What is a variable in algebra?
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What is an algebraic expression?
What is an algebraic expression?
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Study Notes
Key Concepts in Relations and Functions
- Relation: Consists of ordered pairs, establishing a connection between elements from two sets.
- Mapping: Visual representation showing how each domain element corresponds to a range element.
Domain and Range
- Domain: The complete set of x-coordinates or inputs in a relation that can be taken into account.
- Range: The complete set of y-coordinates or outputs resulting from the relation.
Variables in Relations
- Independent Variable: Typically represented as x; its value is chosen freely, influencing the dependent variable.
- Dependent Variable: Typically represented as y; its value changes in response to the independent variable.
Functions
- Function: A specialized type of relation where each input (domain) corresponds to a unique output (range).
- Discrete Function: Comprised of distinct, individual points; not continuous.
- Continuous Functions: Graphable as a single line or smooth curve, indicating unbroken data.
Graphical Analysis
- Vertical Line Test: A method to check if a graph represents a function; it must not intersect the graph more than once.
Functional Representation
- Function Notation: A systematic way to denote a function, typically using an equation format.
- Variable: A symbol (often a letter) that signifies a number within mathematical expressions.
- Algebraic Expression: Combination of numbers, variables, and operational symbols illustrating mathematical relationships.
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