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.

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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 a curve, a circle, or any other shape that is not linear.

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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.

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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.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value).

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What is the vertical line test?

Back

The vertical line test is a method 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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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 of a linear function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented by the value of y when x = 0.

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Can a function have two outputs for the same input?

Back

No, a function cannot have two outputs for the same input. If it does, it is not 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 has a slope of 2 and a y-intercept of 3.