Linear vs. Nonlinear

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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.

Front

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 curves, parabolas, and other shapes.

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How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight line graph, which has a constant slope and does not curve.

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function can be identified by its curved graph, which does not have a constant slope and changes direction.

Front

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

Back

A constant rate of change means that for every unit increase in x, the value of y increases by a fixed amount. This is characteristic of linear functions.

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

Back

A variable rate of change means that the amount by which y changes for each unit increase in x is not constant. This is characteristic of nonlinear functions.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x (rise over run). It indicates the steepness and direction of the line.

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What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis, represented as (0, b) in the equation y = mx + b.

Front

Can a linear function have a y-intercept of (0, 1)?

Back

Yes, a linear function can have a y-intercept of (0, 1). This means that when x = 0, y = 1.

Front

What is an example of a nonlinear function?

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An example of a nonlinear function is y = x^2, which represents a parabola.