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Which statement is false about functions?

A) Functions have inputs and outputs.
B) Each input in a function can have multiple outputs.
C) Functions can be represented by equations, graphs, and tables.
D) All inputs can have the same output.

1 Answer

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Final answer:

The false statement about functions is that each input in a function can have multiple outputs. Functions must have a single unique output for each input, which is a fundamental part of the function's definition.

Step-by-step explanation:

The statement that is false about functions is: B) Each input in a function can have multiple outputs. By definition, in a mathematical function for any given input, there is only one output. This uniqueness of output is an essential characteristic of functions.

Functions have inputs (often referred to as the domain) and outputs (known as the range). Functions can be represented in multiple ways, such as through equations, graphs, and tables, which provides versatility in how they are used and interpreted in various scenarios, including economic models. Differentiating between different types of inputs or factors in a production function is critical, as some may be fixed and others variable. The building in a pizza restaurant example is a fixed input, while the amount of labor could be variable.

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