Identifying Linear and Nonlinear Functions

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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 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 graph can be a curve or any other shape that is not linear.

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How can you identify a linear function from its equation?

Back

A linear function can be identified by its equation, which is in the form y = mx + b. If the highest exponent of the variable is 1, it is linear.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the significance of the slope in a linear function?

Back

The slope (m) in a linear function indicates the rate of change of the function. It represents how much y changes for a unit change in x.

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What does it mean if a function is described as 'nonlinear'?

Back

If a function is described as 'nonlinear', it means that the relationship between the variables does not create a straight line when graphed, indicating a more complex relationship.

Front

What is an example of a nonlinear function?

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An example of a nonlinear function is y = x^2, which produces a parabolic graph.

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How can you determine if a graph is linear or nonlinear?

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You can determine if a graph is linear or nonlinear by checking if it forms a straight line. If it curves or has bends, it is nonlinear.

Front

What is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A and B are not both zero.

Front

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

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A linear equation represents a straight line, while a linear inequality represents a region of the graph that satisfies the inequality, often shaded.