Linear or Nonlinear Functions (graphs and tables)

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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 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?

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 be represented by equations that include exponents, roots, or other non-linear terms.

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How can you determine if a table represents a linear relationship?

Back

To determine if a table represents a linear relationship, check if the rate of change (the difference in y-values divided by the difference in x-values) is constant for all pairs of points.

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What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function, indicating how much y changes for a unit change in x.

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What is the y-intercept in a linear function?

Back

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

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What is an ordered pair in the context of functions?

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An ordered pair is a pair of numbers (x, y) that represents a point on a graph, where x is the input value and y is the output value.

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What is the significance of the ordered pair (-2, 0) in a function table?

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The ordered pair (-2, 0) could prevent the table from being a function if it results in a duplicate x-value with a different y-value, violating the definition of a function.

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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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How can you identify a nonlinear function from its graph?

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A nonlinear function can be identified from its graph by looking for curves, bends, or any shape that is not a straight line.

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What is the importance of identifying linear vs. nonlinear functions in real-world applications?

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Identifying linear vs. nonlinear functions is important in real-world applications because it helps in modeling relationships accurately, predicting outcomes, and making informed decisions based on data.