Linear vs Nonlinear 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 graph can be a curve or any shape that is not a straight line.

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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, which is in the form f(x) = mx + b. If the highest exponent of the variable is 1, it is linear.

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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 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 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?

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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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Can a linear function have a slope of zero?

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Yes, a linear function can have a slope of zero, which means it is a horizontal line. The equation would be of the form f(x) = b, where b is a constant.

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What is the difference between the graphs of linear and nonlinear functions?

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The graph of a linear function is a straight line, while the graph of a nonlinear function can be curved or take on various shapes.

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How do 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 of values, check if the differences between consecutive y-values are constant for equal intervals of x.