Linear vs Nonlinear Functions Review Flashcard

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 graph can be a curve or any other shape that is not linear.

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 the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of y when x = 0.

Front

How can you determine if a function is linear from its equation?

Back

A function is linear if it can be expressed in the form y = mx + b or Ax + By = C, where m and A, B are constants.

Front

What is an example of a linear function?

Back

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

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2 or y = sin(x).

Front

What is the difference between linear and nonlinear graphs?

Back

Linear graphs are straight lines, while nonlinear graphs can be curves or other shapes.

Front

Can a constant function be considered linear?

Back

Yes, a constant function (e.g., y = 5) is considered linear because it can be represented as a horizontal line.