Identifying Linear 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 the form f(x) = 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 form a straight line when graphed. Its graph can be curved or have various shapes, and it does not have a constant rate of change.

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How can you identify a linear function from its graph?

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

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What does the slope of a linear function represent?

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The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

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What is the y-intercept in 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 the value of b in the equation f(x) = mx + b.

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Can a linear function have a negative slope?

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Yes, a linear function can have a negative slope, which means that as the x-value increases, the y-value decreases.

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What is the difference between a linear function and a linear equation?

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A linear function is a specific type of function that produces a straight line when graphed, while a linear equation is an equation that represents a linear 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 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 produces a parabolic curve when graphed.

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How do you determine if a function is linear or nonlinear from a table of values?

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If the differences between consecutive y-values are constant for equal changes in x-values, the function is linear. If the differences vary, the function is nonlinear.