Linear vs 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 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. It has a variable rate of change and can include quadratic, exponential, and other types of functions.

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How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference in 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 significance of the slope in a linear function?

Back

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

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

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is zero.

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Can a linear function have a negative slope?

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

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What is an example of a nonlinear function?

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An example of a nonlinear function is a quadratic function, such as y = x^2, which forms a parabola when graphed.

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How does the graph of a linear function differ from that of a nonlinear function?

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The graph of a linear function is a straight line, while the graph of a nonlinear function can be curved or take on various shapes depending on the type of function.

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What is the formula for a linear function?

Back

The formula for a linear function is typically written as y = mx + b, where m is the slope and b is the y-intercept.

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What does it mean for a function to have a constant rate of change?

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A constant rate of change means that the change in the output (y) is consistent for each unit change in the input (x), characteristic of linear functions.