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

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What does it mean for a relation to be 'Not a Function'?

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

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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-values and y-values. If the differences in y-values divided by the differences in x-values are the same, it is linear.

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How can you identify a Nonlinear Function from a table of values?

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A nonlinear function will show varying rates of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are not constant, it is nonlinear.

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What is the slope of a line in a linear function?

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The slope (m) of a line in a linear function represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

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What is the y-intercept in a linear function?

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The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

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What is the general form of a linear equation?

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The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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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 when graphed.

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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.