Linear and Non-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 rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

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How can you identify a linear function from a graph?

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A linear function can be identified by its straight line graph. If the graph has a constant slope and does not curve, it is linear.

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How can you identify a nonlinear function from a graph?

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A nonlinear function can be identified by its curved graph. If the slope changes at different points, it is nonlinear.

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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, often represented as 'm'.

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What does the y-intercept represent 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 represents the value of the function when x = 0.

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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 does not form a straight line.

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What is a table of values in relation to functions?

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A table of values lists pairs of x and y coordinates that represent points on the graph of a function. It can help determine if a function is linear or nonlinear.

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How can you determine if a function represented by a table is linear?

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A function represented by a table is linear if the differences between consecutive y-values are constant for equal intervals of x.