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Questions and Answers
Which of the following best describes a relation?
Which of the following best describes a relation?
- A rule that relates values from a range to a domain
- A rule that relates values from a domain to a range (correct)
- A set of ordered pairs with the same x-value but different y-value
- A set of ordered pairs with unique x-values
What is the key difference between a relation and a function?
What is the key difference between a relation and a function?
- A relation can have multiple outputs for a given input, while a function has only one output for a given input (correct)
- A relation has only one output for a given input, while a function can have multiple outputs for a given input
- A relation can have multiple inputs for a given output, while a function has only one input for a given output
- A relation and a function are the same thing
How can a function be represented mathematically?
How can a function be represented mathematically?
- As a set of ordered pairs (x, y) with unique x-values (correct)
- As a set of ordered pairs (x, y) with the same y-value but different x-value
- As a set of ordered pairs (x, y) with the same x-value but different y-value
- As a set of ordered pairs (x, y) with unique y-values
What is the role of the domain in a relation or function?
What is the role of the domain in a relation or function?
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What is the range in a relation or function?
What is the range in a relation or function?
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Study Notes
Definition of Relation
- A relation is a set of ordered pairs, where each pair consists of an input and an output.
- It can be represented as a table, graph, or a set notation.
Difference Between Relation and Function
- A relation allows multiple outputs for a single input, while a function has exactly one output for each input.
- This distinction means that in a function, no two ordered pairs can share the same first element.
Mathematical Representation of a Function
- Functions can be represented using various forms, including:
- Equations (e.g., f(x) = 2x + 3)
- Graphs showcasing input-output relationships visually.
- Tables listing inputs alongside their corresponding outputs.
Role of the Domain
- The domain of a relation or function consists of all possible input values (independent variable).
- It defines the limits of the function, determining which values can be used for x in f(x).
Understanding the Range
- The range refers to all possible output values (dependent variable) produced by the relation or function.
- It indicates what values f(x) can take as x varies through the domain.
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