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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x and y values. This means that the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear function?

Back

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

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What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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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.

Tags

CCSS.8.F.A.3

Front

How can you tell if a graph is linear or nonlinear?

Back

A graph is linear if it forms a straight line. If the graph curves or has bends, it is nonlinear.

Tags

CCSS.8.F.A.3

Front

What is the significance of a constant ratio in a linear function?

Back

A constant ratio in a linear function indicates that the relationship between x and y is proportional, meaning that for every increase in x, there is a consistent increase in y.

Tags

CCSS.HSF-LE.A.1B

Front

What does it mean if a function is not a function?

Back

A relation is not a function if there is at least one input (x-value) that corresponds to more than one output (y-value).

Tags

CCSS.8.F.A.1