Linear vs. Nonlinear Functions Day 3

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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 a constant rate of change and 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 create a straight line when graphed. Its rate of change is not constant, and it can be represented by equations that include exponents, roots, or other non-linear terms.

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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 intersects the graph at more than one point, then the graph does not represent a function.

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How can you tell if a table of values represents a linear function?

Back

A table represents a linear function if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

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

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This means no x-value can be paired with more than one y-value.

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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). 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 intersects the y-axis. It is the value of y when x is 0.

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What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola and does not create a straight line when graphed.

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What is a common characteristic of nonlinear graphs?

Back

Nonlinear graphs often have curves, bends, or changes in direction, indicating that the relationship between x and y is not constant.

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What is a linear equation?

Back

A linear equation is an equation that represents a linear function. It can be written in the form Ax + By = C, where A, B, and C are constants.