Multiple Choice
Which of the following best describes a function in the context of business calculus?
0. Functions
Introduction to Functions
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Which of the following is NOT a property of a mathematical function?
A
The domain is the set of all possible inputs.
B
Each input has exactly one output.
C
A function can assign multiple outputs to a single input.
D
The range is the set of all possible outputs.
Verified step by step guidance1
Step 1: Begin by understanding the definition of a mathematical function. A function is a relation where each input (from the domain) is assigned to exactly one output (in the range).
Step 2: Review the properties of a function: (1) The domain is the set of all possible inputs, (2) Each input has exactly one output, and (3) The range is the set of all possible outputs.
Step 3: Analyze the statement 'A function can assign multiple outputs to a single input.' This contradicts the definition of a function, as a function must assign exactly one output to each input.
Step 4: Conclude that the statement 'A function can assign multiple outputs to a single input' is NOT a property of a mathematical function.
Step 5: Verify the other statements to ensure they align with the definition of a function: The domain is the set of all possible inputs, and the range is the set of all possible outputs. Both are valid properties of a function.
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