Functions, Domain, and Range

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

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How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) corresponds to exactly one output (y-value). This can be checked using the vertical line test.

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What does it mean for a function to be linear?

Back

Front

What does it mean for a function to be nonlinear?

Back

A nonlinear function is a function that does not form a straight line when graphed. Examples include quadratic, exponential, and logarithmic functions.

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What is an increasing function?

Back

An increasing function is a function where, as the input values increase, the output values also increase.

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What is a decreasing function?

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A decreasing function is a function where, as the input values increase, the output values decrease.

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What is a positive function?

Back

A positive function is a function where the output values are greater than zero for all inputs in its domain.

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What is a negative function?

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A negative function is a function where the output values are less than zero for all inputs in its domain.