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Questions and Answers
What distinguishes a relation from a function?
What distinguishes a relation from a function?
- A relation cannot be represented using graphs.
- A function has a specific output for each input. (correct)
- A relation can have multiple outputs for one input. (correct)
- A function cannot have a domain.
Which of the following is an example of a function?
Which of the following is an example of a function?
- The relation that maps every person to their age.
- The relation that maps a number to its square root. (correct)
- The relation that maps students to their grades.
- The relation that maps a city to its population size.
If a relation is expressed as a set of ordered pairs, which condition must it satisfy to be a function?
If a relation is expressed as a set of ordered pairs, which condition must it satisfy to be a function?
- All ordered pairs must have distinct second elements.
- At least one pair must include zero.
- No two pairs can have the same first element. (correct)
- All ordered pairs must contain integers.
In the context of graphs, how can a function be identified?
In the context of graphs, how can a function be identified?
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Which statement best describes the domain of a function?
Which statement best describes the domain of a function?
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Study Notes
Relations and Functions
- A relation is a set of ordered pairs that associates elements from one set to another.
- A function is a special type of relation where each input (first element in the ordered pair) has exactly one output (second element in the ordered pair).
Identifying Functions
- A relation expressed as a set of ordered pairs is a function if no two ordered pairs have the same first element but different second elements.
- In a graph, a function can be identified using the vertical line test. If any vertical line intersects the graph at more than one point, it is not a function.
Domain of a Function
- The domain of a function is the set of all possible input values for which the function is defined.
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Description
Test your understanding of the distinctions between relations and functions. This quiz covers key concepts such as identifying functions from sets of ordered pairs, their graph representations, and the definition of a function's domain. Perfect for students reviewing foundational topics in mathematics.
