Linear and 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 graph can be curved or have varying slopes.

Front

How can you identify a linear function from its graph?

Back

A linear function's graph will always be a straight line, regardless of its position on the coordinate plane.

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function's graph will show curves, bends, or changes in direction, indicating it is not a straight line.

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 line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

Give an example of a linear function.

Back

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

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is y = x^2 + 2.

Front

What is the difference between a linear and a nonlinear table of values?

Back

A linear table of values will show a constant rate of change, while a nonlinear table will show varying rates of change.