Functions, Functions, Functions 2.0

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What is a function?

Back

A function is a relation where every input has only ONE output.

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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 linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.

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What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and can include curves, parabolas, etc.

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What does the vertical line test determine?

Back

The vertical line test determines if a graph represents a function; if a vertical line crosses the graph more than once, it is not a function.

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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 the function.

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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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What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for every x, there is a unique y.

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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.