Identifying 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 a curve or any other shape that is not linear.

Front

Identify the type of function: y = 2x + 3

Back

Linear

Front

Identify the type of function: y = x^2 - 5x + 6

Back

Nonlinear

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of y with respect to x. It indicates how steep the line is.

Front

What is the y-intercept 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

Identify the type of function: y = 4x^3 - 2x + 1

Back

Nonlinear

Front

Identify the type of function: y = -3x + 7

Back

Linear

Front

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

Back

Linear functions have graphs that are straight lines, while nonlinear functions have graphs that are curves or other shapes.