Is the Relation a Function?

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

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How can you determine if a relation is a function?

Back

A relation is a function if no x-value is paired with more than one y-value.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, the curve is not a function.

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What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one x-value is associated with multiple y-values.

Front

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 corresponds to only one y-value.

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What is an example of a function?

Back

An example of a function is the equation y = 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?

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

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What is a mapping in the context of functions?

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A mapping is a representation of how each element in one set (domain) is paired with elements in another set (range).

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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?

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