Linear and 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 a constant rate of change and can be expressed in 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 create a straight line when graphed. Its rate of change is not constant, and it can be represented by equations that include exponents, roots, or other non-linear terms.

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How can you determine if a graph is linear or nonlinear?

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You can determine if a graph is linear or nonlinear by checking if it forms a straight line. If the graph curves or has bends, it is nonlinear.

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

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A relation is a function if every input (x-value) has exactly one output (y-value). This means that no x-value is repeated with different y-values.

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What is the slope of a linear function?

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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 is the y-intercept of a linear function?

Back

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

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Can a nonlinear function be a function?

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Yes, a nonlinear function can still be a function as long as each input has exactly one output. For example, y = x^2 is a nonlinear function that is still 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 y = 2x + 3. This function has a constant 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 y = x^2. This function creates a parabolic curve when graphed.

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What is the difference between a function and not a function?

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A function has one output for each input, while a relation that is not a function has at least one input with multiple outputs.