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, cubic, or exponential.

Tags

CCSS.8.F.A.3

Front

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/run).

Tags

CCSS.8.EE.B.5

Front

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

Back

A relation is a function if each input (x-value) has exactly one output (y-value). If an input has multiple outputs, it is not a function.

Tags

CCSS.8.F.A.1

Front

What is the y-intercept in a linear function?

Back

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

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 constant, it is linear.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is paired with exactly one output.

Tags

CCSS.8.F.A.1

Front

What does it mean for a graph to be nonlinear?

Back

A nonlinear graph does not form a straight line and can curve or change direction. Examples include parabolas and circles.

Tags

CCSS.8.F.A.3

Front

What is a quadratic function?

Back

A quadratic function is a type of nonlinear function that can be expressed in the form y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is a cubic function?

Back

A cubic function is a nonlinear function that can be expressed in the form y = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.