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 a constant rate of change and can be expressed in 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 create a straight line when graphed. The rate of change is not constant, and it can be represented by equations that include exponents, roots, or other non-linear terms.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference in the y-values for equal intervals in the x-values. This means the ratio of the change in y to the change in x is constant.

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.

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 the value of y when x is 0.

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 an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.

Front

How can you tell if a graph represents a linear function?

Back

A graph represents a linear function if it forms a straight line. If the graph curves or bends, it is nonlinear.

Front

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

Back

A linear relationship has a constant rate of change and can be represented by a straight line, while a nonlinear relationship has a variable rate of change and cannot be represented by a straight line.

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if the y-values rise as the x-values increase, and it is decreasing if the y-values fall as the x-values increase.