Podcast
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?
- The domain is the set of all possible input values.
- Each input value has only one output value.
- The range is the set of all possible output values.
- Each output value can be paired with multiple input values. (correct)
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?
- Yes, because each input value has only one output value. (correct)
- No, because the output value 3 is paired with two different input values.
- Yes, because all the input values are different and the output values are different.
- No, because the domain and range have different numbers of elements.
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?
- {1, 2, 3, 4, 5}
- {1, 2, 3, 4} (correct)
- {2, 3, 4, 5}
- {1, 2, 3, 4, 5, 2, 3, 4, 5}
Which of the following sets of ordered pairs represents a function?
Which of the following sets of ordered pairs represents a function?
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?
Flashcards
Function
Function
A relation where each input has one unique output.
Domain
Domain
The set of input values for a function.
Range
Range
The set of output values that a function can produce.
Relation That Is Not a Function
Relation That Is Not a Function
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Identifying Functions
Identifying Functions
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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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