Multiple Choice
State the inputs and outputs of the following relation. Is it a function? {}
0. Functions
Introduction to Functions
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Which of the following best describes a function in mathematics?
A
A set of ordered pairs with no restrictions.
B
A relation where each input has exactly one output.
C
A relation where each output has exactly one input.
D
A process that assigns multiple outputs to a single input.
Verified step by step guidance1
Step 1: Understand the definition of a function in mathematics. A function is a relation where each input (from the domain) is assigned to exactly one output (in the range). This means no input can have more than one output.
Step 2: Analyze the first option: 'A set of ordered pairs with no restrictions.' This is incorrect because a function must follow the rule that each input has exactly one output, which is a restriction.
Step 3: Analyze the second option: 'A relation where each input has exactly one output.' This is correct because it aligns with the definition of a function in mathematics.
Step 4: Analyze the third option: 'A relation where each output has exactly one input.' This is incorrect because a function does not require that each output be associated with only one input. Multiple inputs can share the same output.
Step 5: Analyze the fourth option: 'A process that assigns multiple outputs to a single input.' This is incorrect because a function cannot assign more than one output to a single input, as it violates the definition of a function.
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