Linear versus 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 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. Its rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

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How can you identify a linear function from its graph?

Back

A linear function will graph as a straight line. It will have a constant slope and will not curve.

Front

How can you identify a nonlinear function from its graph?

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A nonlinear function will graph as a curve or a line that changes direction. It does not have a constant slope.

Front

What is the slope of a linear function?

Back

The slope of a linear function (m) 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 of a linear function represent?

Back

The y-intercept (b) of a linear function is the point where the graph intersects the y-axis. It represents the value of the function when x = 0.

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Can a function be both linear and nonlinear?

Back

No, a function cannot be both linear and nonlinear. It is classified as one or the other based on its characteristics.

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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 graphs as a straight line.

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What is an example of a nonlinear function?

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An example of a nonlinear function is f(x) = x^2, which graphs as a parabola.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).