Linear and Nonlinear Functions

Front

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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How can you determine if a graph represents a function?

Back

A graph represents a function if every vertical line drawn through the graph intersects it at most once. This is known as the vertical line test.

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What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run). It indicates how much y changes for a unit change in x.

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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. It represents the value of the function when x = 0.

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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). A relation can have multiple outputs for a single input.

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What is an example of a linear function?

Back

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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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, the function is linear.

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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.