Linear or Non-Linear?

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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 f(x) = 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. It can have curves, bends, or other shapes, and does not fit the form f(x) = mx + b.

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How can you determine if a function is linear or nonlinear from a table of values?

Back

To determine if a function is linear from a table, check if the differences between consecutive y-values are constant for equal intervals of x. If they are constant, the function is linear.

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What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run). It represents the rate of change of the function.

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What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It represents the value of the function when x = 0.

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Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which indicates that as x increases, y decreases.

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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 = 0, where A, B, and C are constants.

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

Back

A linear equation represents a relationship between variables, while a linear function is a specific type of linear equation that defines a function with a unique output for each input.

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How can you identify a nonlinear function from its graph?

Back

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 a quadratic function?

Back

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