Linear and Non Linear 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 graph can be curved or have varying slopes.

Front

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

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are constant, the function is linear.

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 y changes for a unit change in x.

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 represented by the value of b in the equation f(x) = mx + b.

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 f(x) = 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 and has a constant slope.

Front

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

Back

A linear graph is a straight line, while a nonlinear graph can be curved or have varying slopes.

Front

What is a common characteristic of nonlinear functions?

Back

Nonlinear functions often have changing rates of change and can include curves, circles, or other shapes.