Linear or Non-Linear?

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What is a linear function?

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A linear function is a function that can be represented by a straight line on a graph. It has a constant rate of change and can be expressed in the form y = 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 be represented by equations that include exponents, roots, or other non-linear terms.

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What is the vertical line test?

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The vertical line test is a method used to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, then the graph does not represent a function.

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What is the horizontal line test?

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The horizontal line test is used to determine if a function is one-to-one. If any horizontal line intersects the graph more than once, the function is not one-to-one.

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What does it mean for a function to be one-to-one?

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A one-to-one function is a function where each output value is paired with exactly one input value. This means that no two different inputs produce the same output.

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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 difference between the y-values for equal intervals of x-values. If the differences are not constant, the function 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 and direction. It is calculated as the change in y divided by the change in x (rise over run).

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What is the y-intercept of a linear function?

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The y-intercept is the point where the graph of a function crosses the y-axis. It is represented by the value of y when x is 0 in the equation of the function.

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Can a function be both linear and nonlinear?

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No, a function cannot be both linear and nonlinear. A function is classified as either linear or nonlinear based on its characteristics and graph.

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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.