Linear and Nonlinear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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. Examples include quadratic functions (y = x^2) and cubic functions (y = x^3).

Front

Identify the linear function from the following: y = 2x + 3, y = |x|, y = x^2, y = x^3 - 1.

Back

y = 2x + 3 is the linear function.

Front

What is the slope of the linear function y = 3x + 4?

Back

The slope (m) of the function y = 3x + 4 is 3.

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, represented by the value of b in the equation y = mx + b.

Front

Which of the following is NOT a function: y = x^2, y = 2x + 3, y = |x|, or y = x + 1?

Back

All of the given equations are functions.

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

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

Front

Provide an example of a nonlinear function.

Back

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

Front

What is the domain of the function y = 2x + 3?

Back

The domain of the function y = 2x + 3 is all real numbers.