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 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, a circle, or any other shape that 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 over run (change in y over 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 f(x) = 2x + 3.

Front

Give an example of a nonlinear function.

Back

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

Front

What is the difference between the graphs of linear and nonlinear functions?

Back

The graph of a linear function is a straight line, while the graph of a nonlinear function can be curved or take various shapes.

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 in a table.

Front

What is a quadratic function?

Back

A quadratic function is a type of nonlinear function that can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.