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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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