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Questions and Answers
Which of the following is NOT a characteristic of a function?
Which of the following is NOT a characteristic of a function?
Consider the following relation: {(1, 3), (2, 5), (3, 3), (4, 7)}. Is this relation a function?
Consider the following relation: {(1, 3), (2, 5), (3, 3), (4, 7)}. Is this relation a function?
A set of ordered pairs is given: {(1, 2), (2, 3), (3, 4), (4, 5)}. What is the domain of this relation?
A set of ordered pairs is given: {(1, 2), (2, 3), (3, 4), (4, 5)}. What is the domain of this relation?
Which of the following sets of ordered pairs represents a function?
Which of the following sets of ordered pairs represents a function?
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If a relation is a function, which of the following statements is ALWAYS TRUE?
If a relation is a function, which of the following statements is ALWAYS TRUE?
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Study Notes
Functions and Relations
- A relation is a function if each input (domain) value has only one output (range) value.
Domain and Range
- Domain: The set of all possible input values.
- Range: The set of all possible output values.
Example of a Relation That Is Also a Function
- Domain: {1, 2, 3}
- Range: {2, -7}
- Relation: (1, 2), (2, 2), (3, -7)
- This is a function because every input value has only one output.
Example of a Relation That Is NOT a Function
- Domain: {1, 2}
- Range: {2, -3, 4}
- Relation: (1, 2), (2, -3), (1, 4)
- This is not a function because the input value 1 is associated with two different output values (2 and 4).
Identifying Functions
- To determine if a relation is a function, check if each input value maps to exactly one output value.
- If any input value is associated with multiple outputs, the relation is not a function.
Example: Determining if a Set of Points Represents a Function
- Domain: {-3, -2, 0, 3}
- Range: {2, 4, 5, 6, 8}
- Points: (-3, 2), (-2, 4), (0, 5), (-2, 6), (3, 8)
- This relation is not a function because the input value -2 is associated with two different output values (4 and 6).
- A function must assign a unique output to each input.
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Description
Test your understanding of functions and relations with this quiz. Explore concepts like domain, range, and criteria for a relation to be classified as a function. Perfect for those studying mathematics at various levels.
