Functions

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What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

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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) that the function can accept.

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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 no two ordered pairs have the same first element (x-value) with different second elements (y-values).

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What is a vertical line test?

Back

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

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What does it mean if a graph is a function?

Back

If a graph is a function, it means that for every x-value, there is exactly one corresponding y-value.

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

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If a graph is not a function, it means that there is at least one x-value that corresponds to more than one y-value.

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What is an example of a function?

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An example of a function is f(x) = 2x + 3, where for each x-value, there is 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 y^2 = x, where a single x-value can correspond to two different y-values.

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What is a mapping diagram?

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A mapping diagram visually represents the relationship between the domain and range of a function, showing how each input is paired with an output.