Linear vs Nonlinear functions

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What is a linear function?

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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?

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A nonlinear function is a function that does not create a straight line when graphed. The 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 identify a linear function from a table of values?

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A linear function will have a constant rate of change between the x-coordinates and y-coordinates. This means that the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

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What does it mean if a function is not a function?

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A relation is not a function if at least one input (x-value) corresponds to more than one output (y-value). This violates the definition of a function.

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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 is calculated as the change in y divided by the change in x (rise/run).

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What is the y-intercept of a linear function?

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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 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, indicating that it is not linear.

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How can you tell if a graph represents a linear function?

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A graph represents a linear function if it forms a straight line. If the graph curves or has bends, it is a nonlinear function.

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What is the relationship between linear functions and their graphs?

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The graph of a linear function is always a straight line, which indicates a constant rate of change between the variables.