Relations, Functions, & Linear vs. Nonlinear

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What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x-value) and an output (y-value).

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What is a function?

Back

A function is a special type of relation where each input (x-value) is associated with exactly one output (y-value).

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How can you determine if a relation is a function?

Back

A relation is a function if no x-value is repeated with different y-values.

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What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, with a constant rate of change.

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What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed, indicating a variable rate of change.

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What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x, representing the steepness of the line.

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What does it mean for a function to be increasing?

Back

A function is increasing if, as the x-values increase, the y-values also increase.

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What does it mean for a function to be decreasing?

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A function is decreasing if, as the x-values increase, the y-values decrease.

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What is the vertical line test?

Back

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

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What is a mapping diagram?

Back

A mapping diagram visually represents the relationship between inputs and outputs in a function, showing how each x-value is paired with a y-value.