Linear or Nonlinear (Graphs)

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What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 graph to a straight line. Its graph can be a curve, a circle, or any other shape that is not a straight line.

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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?

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A nonlinear function can be identified by its curved graph, which does not have a constant slope.

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

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A graph is 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.

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What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is. It is calculated as the change in y divided by the change in x (rise over run).

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What is the y-intercept of a linear function?

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

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What is an example of a linear function?

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An example of a linear function is y = 2x + 3, which graphs to 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 y = x^2, which graphs to a parabola.

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input has exactly one output, while a relation can have multiple outputs for a single input.