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 f(x) = 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 table of values?

Back

A linear function will have a constant rate of change, meaning the ratio of the change in y to the change in x will be the same for all intervals.

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, representing the value of the function when x = 0.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which represents a quadratic function.

Front

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

Back

A graph represents a linear function if it forms a straight line and passes the vertical line test, meaning any vertical line intersects the graph at most once.

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 is the significance of the ratio of change in y to change in x in determining linearity?

Back

If the ratio of change in y to change in x is constant across all intervals, the function is linear; if it varies, the function is nonlinear.