Linear vs Nonlinear Functions

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Tags

CCSS.8.F.A.1

Front

How can you tell if a relation is a function?

Back

A relation is a function if no x-value is paired with more than one y-value.

Tags

CCSS.8.F.A.1

Front

What does it mean if an x-value is repeated in a relation?

Back

If an x-value is repeated with different y-values, the relation is not a function.

Tags

CCSS.8.F.A.1

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.

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 graph to a straight line and may include curves or other shapes.

Tags

CCSS.8.F.A.3

Front

Give an example of a linear function.

Back

An example of a linear function is y = 2x + 3.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is y = x^2.

Tags

CCSS.8.F.A.3

Front

What is the slope in a linear function?

Back

The slope (m) is the rate of change of y with respect to x, indicating how steep the line is.

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept (b) is the point where the line crosses the y-axis, representing the value of y when x = 0.

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.

Tags

CCSS.HSF-LE.A.1B