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 a curve, a circle, or any other shape that is not a straight line.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight-line graph. If the graph has a constant slope and does not curve, it is linear.

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function can be identified by its curved graph. If the graph changes direction or has varying slopes, it is nonlinear.

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 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.

Front

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

Back

A linear equation has a constant rate of change and graphs as a straight line, while a nonlinear equation has a variable rate of change and graphs as a curve.