Function or Not a Function

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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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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) has more than one output (y-value).

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How can you determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

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What is the vertical line test?

Back

The vertical line test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

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Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

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What is an example of a function?

Back

An example of a function is f(x) = x + 2, 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 {(1, 2), (1, 3)}, where the input 1 has two different outputs.

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What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with its output.

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What is a table of values?

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A table of values lists pairs of input and output values, which can help determine if a relation is a function.

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What is the definition of a domain in a function?

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The domain of a function is the set of all possible input values (x-values) that the function can accept.