Linear vs. Nonlinear Functions

Front

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 graph?

Back

A linear function can be identified from a graph if the points form a straight line. Additionally, the slope between any two points on the line remains constant.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What are the characteristics of a nonlinear graph?

Back

Nonlinear graphs can curve, bend, or change direction. They do not have a constant slope and can represent various types of relationships, such as quadratic or exponential.

Tags

CCSS.8.F.A.3

Front

What is the significance of the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Tags

CCSS.8.EE.B.5

Front

What does it mean for a function to be represented by a table?

Back

A function represented by a table shows the relationship between the independent variable (x) and the dependent variable (y) through pairs of values. Each x-value corresponds to one y-value.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

How can you determine if a table represents a linear function?

Back

To determine if a table represents a linear function, check if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

A linear equation represents a straight line and has a constant rate of change, while a nonlinear equation represents a curve and has a variable rate of change.

Tags

CCSS.8.F.A.3

Front

What are some examples of nonlinear functions?

Back

Examples of nonlinear functions include quadratic functions (e.g., y = x^2), exponential functions (e.g., y = 2^x), and trigonometric functions (e.g., y = sin(x)).

Tags

CCSS.8.F.A.3