NOWAK Linear vs. Nonlinear functions

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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. It has the form y = mx + b, where m is the slope and b is the y-intercept.

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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. Its graph can be a curve or any shape that is not a straight line.

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How can you identify a linear function from a graph?

Back

A linear function can be identified by its straight-line graph. If the graph is not straight, it is not a linear function.

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

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

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What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents 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 the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

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What is the y-intercept?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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Can a function have more than one y-value for a single x-value?

Back

No, a function cannot have more than one y-value for a single x-value. If it does, it is not a function.

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What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which has a slope of 2 and a y-intercept of 3.

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What is an example of a nonlinear function?

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An example of a nonlinear function is f(x) = x^2, which forms a parabola when graphed.