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Functions and Relations Classification
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Functions and Relations Classification
A relation is a function when every input is paired with exactly one output. Different inputs may share an output.
Function or Not a Function?
Choose the best answer for each relation.
1.A relation pairs inputs 2, 4, 6, and 8 with outputs 3, 6, 9, and 12, in that order. Is this relation a function?
- Yes, each input has exactly one output.
- No, an input is paired with more than one output.
2.The ordered pairs (1, 8), (3, 10), (1, 14), and (5, 12) form a relation. Is it a function?
- Yes, each input has exactly one output.
- No, the input 1 has two different outputs.
3.At a wildlife sanctuary, ticket codes A, B, and C are paired with entry gates North, East, and South, respectively. Is the relation from ticket codes to assigned gates a function?
- Yes, each ticket code is paired with one gate.
- No, two different ticket codes cannot use the same gate.
4.Which relation is a function?
- 1 → A, 2 → B, 3 → C
- 1 → A, 1 → B, 2 → C
- 1 → A, 2 → A, 2 → C
Analyze and Explain
Use the definition of a function to complete and explain each response.
5.The rule for a function is to add 4 to each input. Complete the output for inputs 1, 2, 3, and 4: 5, 6, __, 8.
6.Consider the relation {(2, 4), (4, 7), (6, 10), (4, 13)}. Is it a function? Explain your answer.
7.Write four ordered pairs that make a relation that is not a function. Include one input paired with two different outputs.
8.At a wildlife sanctuary, the same number of hours spent observing animals can lead to different numbers of species recorded by different visitors. Is the relation from observation hours to species recorded necessarily a function? Explain.
Challenge Problems
Look carefully at the input values in each relation.
9.Select all the relations that are functions.
- {(1, 2), (2, 4), (3, 6), (4, 8)}
- {(-2, 5), (0, 5), (2, 5), (4, 5)}
- {(3, 1), (3, 7), (5, 2), (6, 4)}
10.A function machine multiplies each input by 4, then subtracts 1. Find the outputs for inputs 0, 1, 2, and 3.
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