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 f(x) = 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-values and y-values. If the differences in y-values divided by the differences in x-values are the same, the function is linear.

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.

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CCSS.8.EE.B.5

Front

What is the y-intercept of 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 f(x) = mx + b.

Front

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.

Front

What is the difference between a linear graph and a nonlinear graph?

Back

A linear graph is a straight line, indicating a constant rate of change, while a nonlinear graph can be curved or have varying slopes, indicating a changing rate of change.

Tags

CCSS.8.F.A.3

Front

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

Back

You can determine if a graph is linear or nonlinear by checking if it forms a straight line. If it curves or has bends, it is nonlinear.

Tags

CCSS.8.F.A.3

Front

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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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which represents a parabola and is not a straight line.

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CCSS.8.F.A.3