From functions to Linear vs. Non-Linear

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What is a function?

Back

A function is a relation where each input (x) has exactly one output (y).

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What does it mean for a relation to be a function?

Back

A relation is a function if every input is paired with one and only one output.

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What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b.

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What is a non-linear function?

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A non-linear function is a function that does not graph to a straight line, such as quadratic or exponential functions.

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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 crosses the curve 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) for the function.

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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) that the function can produce.

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

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

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What is an example of a linear function?

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An example of a linear function is f(x) = 2x + 3.

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What is an example of a non-linear function?

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An example of a non-linear function is f(x) = x^2.