Is it a Function?

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What is a function in mathematics?

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.

Tags

CCSS.8.F.A.1

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How can you determine if a set of ordered pairs represents a function?

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A set of ordered pairs represents a function if no two different pairs have the same first element (input).

Tags

CCSS.8.F.A.1

Front

What is the vertical line test?

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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, then the curve is not a function.

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

Back

A relation is 'not a function' if at least one input is associated with more than one output.

Tags

CCSS.8.F.A.1

Front

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 corresponds to only one output.

Tags

CCSS.8.F.A.1

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What is an example of a function?

Back

An example of a function is f(x) = x^2, where each input x has a unique output x^2.

Tags

CCSS.8.F.A.1

Front

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

Back

An example of a relation that is not a function is the set of ordered pairs {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.

Tags

CCSS.8.F.A.1

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What is a one-to-one function?

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A one-to-one function is a function where each output is associated with exactly one input, meaning no two different inputs produce the same output.

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What is a many-to-one function?

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A many-to-one function is a function where multiple inputs can produce the same output.

Tags

CCSS.8.F.A.1

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What is the domain of a function?

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