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.

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.

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.

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.

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.

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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.

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.

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.

Front

What are some examples of nonlinear functions?

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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)).