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Questions and Answers
What is the domain?
What is the domain?
The first element (x-value) of a relation or function; also known as the input.
What is a function?
What is a function?
A function is a relation such that for each first element (x-value, input) there exists one and only one (unique) second element.
What is the input in a relation or function?
What is the input in a relation or function?
The x-value of a relation or function.
What is the output in a relation or function?
What is the output in a relation or function?
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What is the range?
What is the range?
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What defines a relation?
What defines a relation?
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A relation can be a function.
A relation can be a function.
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A function can have the same x-value for different outputs.
A function can have the same x-value for different outputs.
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A relation consists of ordered pairs that can be graphed on a coordinate _____ plane.
A relation consists of ordered pairs that can be graphed on a coordinate _____ plane.
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Give an example of a set that is considered a relation but not a function.
Give an example of a set that is considered a relation but not a function.
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Study Notes
Domain and Functions
- Domain: Refers to the x-values (inputs) of a relation or function.
- Function: A specific type of relation where each x-value correlates with one unique y-value, meaning no repetition of x-values occurs in ordered pairs.
Input and Output
- Input: Represents the x-value in a relation or function.
- Output: Represents the y-value in a relation or function.
Range and Relation
- Range: Consists of the y-values (outputs) of a relation or function.
- Relation: Any set of numbers represented on a coordinate plane (x, y) that can sometimes be a function but isn't necessarily one.
Concept of a Function
- A function mandates that each input yields only one output, reflecting real-world restrictions, like a person’s weight being singular at any given time.
- An example of a function includes paired elements like (0, 2), (4, 9), (6, 12), and (7, 2), where each x-value has a single corresponding y-value.
Identifying Functions
- Situations where multiple inputs produce the same output (like a car starting and ending at the same position) still qualify as functions if each input leads to a singular output.
- Non-functional examples arise when a single input corresponds to multiple outputs, illustrated by pairs like (0, 2), (4, 9), (5, 6), (5, 8), showing that 5 produces two different outputs.
Graphical Representation
- Graphs of two-variable equations consist of points represented as ordered pairs, forming a relation.
- For infinite ordered pairs, the relation is best expressed through the rule method or the equation itself, while finite sets work well with the list method.
Example Relations
- Example 1: Set A = {(6, 2), (2, 6), (4, 1), (4, 0)} is a relation since it contains ordered pairs. However, it is not a function due to repetitive x-values (4 appears twice).
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Description
Test your understanding of functions, domain, and range with this quiz! Explore the concepts of input and output values, and how they relate to real-world applications. Determine if the given sets of numbers represent functions or just relations.
