Linear or Nonlinear Function

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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, a circle, or any other shape that is not a straight line.

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What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x). 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?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

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How can you determine if a function is linear from its graph?

Back

A function is linear if its graph is a straight line. If the graph curves or has any bends, the function is nonlinear.

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What is a quadratic function?

Back

A quadratic function is a type of nonlinear function that can be expressed in the form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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

Back

A linear function has a constant rate of change and graphs as a straight line, while a quadratic function has a variable rate of change and graphs as a parabola.

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What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input variable.

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How can you identify a nonlinear function algebraically?

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A nonlinear function can be identified algebraically if it contains variables raised to a power greater than one, products of variables, or functions like sine, cosine, etc.