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, a circle, or any other shape that is not linear.

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How can you identify a linear function from its equation?

Back

If the equation can be written in the form y = mx + b, where m and b are constants, it is a linear function.

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What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by 'm' in the equation y = mx + b. It indicates how much y changes for a unit change in x.

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What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is represented by 'b' in the equation y = mx + b.

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

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How can you determine if a relation is a function using the vertical line test?

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If a vertical line drawn through the graph of the relation intersects the graph at more than one point, then the relation is not a function.

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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, which represents a straight line with 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 represents a parabola and is not a straight line.

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What does it mean for a function to be increasing?

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A function is increasing if, as the input (x) increases, the output (y) also increases. This is typically seen in linear functions with a positive slope.