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 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. Its graph can be curved or have varying slopes.

Front

How can you identify a linear function from its graph?

Back

A linear function's graph is a straight line, and it passes the vertical line test, meaning any vertical line intersects the graph at most once.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line crosses the graph more than once, it is not a function.

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What does it mean for y to be a function of x?

Back

It means that for every input value of x, there is exactly one output value of y.

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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).

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What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation y = mx + b.

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Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input. This would violate the definition of a function.

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What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which represents a straight line when graphed.

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What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which represents a parabola when graphed.