12/10 Identifying Functions

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

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How can you identify a function from a graph?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is the Vertical Line Test?

Back

The Vertical Line Test states that if a vertical line intersects a graph more than once, the graph does not represent a function.

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What does it mean if a relation is not a function?

Back

A relation is not a function if at least one input (x-value) is associated with more than one output (y-value).

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Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value has only one corresponding y-value.

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What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

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What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the x-value 1 has two different y-values.

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What is the definition of a domain in 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 definition of a range in a function?

Back

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

Front

How do you determine if a set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no x-value is repeated with a different y-value.