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 graph can be curved or have varying slopes.

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 are the characteristics of a linear function's graph?

Back

The graph of a linear function is a straight line, has a constant slope, and intersects the y-axis at the y-intercept.

Front

What are the characteristics of a nonlinear function's graph?

Back

The graph of a nonlinear function can be curved, may have varying slopes, and does not have a constant rate of change.

Front

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

Back

If the equation can be rearranged into the form y = mx + b, it is linear. If it includes variables raised to powers other than one, or products of variables, it is nonlinear.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x (rise over run) and indicates the steepness of the line.

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

Can a linear function have a slope of zero?

Back

Yes, a linear function can have a slope of zero, which means it is a horizontal line.

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.