4-3 Linear vs. Non-Linear Functions

Front

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 graph can be curved or have various shapes, and it does not have a constant rate of change.

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How can you identify a linear function from a graph?

Back

A linear function can be identified by its straight-line graph. If the graph is not straight, it is not a linear function.

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if every input (x-value) has exactly one output (y-value). This means that no vertical line can intersect the graph at more than one point.

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 crosses the graph at more than one point, it is not a function.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by 'm' in the equation f(x) = mx + b. It indicates 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. It is represented by 'b' in the equation f(x) = mx + b.

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Can a function be both linear and nonlinear?

Back

No, a function cannot be both linear and nonlinear. A function is classified as either linear or nonlinear based on its graph and equation.

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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 with a slope of 2 and a y-intercept of 3.

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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 represents a parabola and does not form a straight line.