Linear/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-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.

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.

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 and a nonlinear graph?

Back

A linear graph is a straight line, indicating a constant rate of change, while a nonlinear graph is curved or has bends, indicating a variable rate of change.

Tags

CCSS.8.F.A.3

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means that as the x-value increases, the y-value decreases.

Tags

CCSS.8.EE.B.5

Front

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 do you determine if a graph is linear or nonlinear?

Back

To determine if a graph is linear or nonlinear, check if the graph forms a straight line. If it does, it is linear; if it curves or bends, it is nonlinear.

Tags

CCSS.8.F.A.3