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 can include quadratic, exponential, and other types of functions.

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

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To determine if a function is linear from a table, check if the differences between consecutive y-values are constant for equal intervals of x. If they are constant, the function is linear; if not, 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 a measure of its steepness, represented by 'm' in the equation f(x) = mx + b. It is calculated as the change in y divided by the change in x (rise/run).

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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 is represented by 'b' in the equation f(x) = mx + b.

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What is the rate of change in a linear function?

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The rate of change in a linear function is constant and is equal to the slope of the line. It indicates how much the output (y) changes for a unit change in the input (x).

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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 indicates that as the value of x increases, the value of y decreases.

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What is an example of a nonlinear function?

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An example of a nonlinear function is a quadratic function, such as f(x) = x^2, which produces a parabolic graph.

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How do you identify a linear function from its graph?

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A linear function can be identified from its graph as a straight line. If the graph curves or bends, it is not linear.

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

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A linear equation is an equation that represents a straight line, while a linear function is a specific type of linear equation that defines a relationship between two variables.