Linear vs Nonlinear functions

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What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. 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 create a straight line when graphed. It may have a variable rate of change and can include curves, parabolas, and other shapes.

Front

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

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function, indicating how much y changes for a unit change in x.

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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 crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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What is the difference between a function and a non-function?

Back

A function assigns exactly one output for each input, while a non-function may assign multiple outputs for a single input.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

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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 an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which creates a parabolic curve when graphed.

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

Back

A function has a constant rate of change if the difference in y-values divided by the difference in x-values is the same for any two points on the line.