Identifying Linear 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 f(x) = 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 curved or have varying slopes.

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How can you identify a linear function from its equation?

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A linear function can be identified by its equation being in the form f(x) = mx + b, where m and b are constants.

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What is the slope of a linear function?

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The slope of a linear function is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line.

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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, represented by the value of b in the equation f(x) = 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).

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How can you determine if a graph represents a function?

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You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

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What are some examples of linear functions?

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Examples of linear functions include f(x) = 2x + 3, f(x) = -x + 5, and f(x) = 0.5x.

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What are some examples of nonlinear functions?

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Examples of nonlinear functions include f(x) = x^2, f(x) = sin(x), and f(x) = e^x.

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What is the significance of the slope in real-world applications?

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The slope represents the rate of change, which can indicate speed, growth, or any other change in quantity over time.