4.7 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 curved or have varying slopes.

Front

Identify the function type: y = 2x + 3

Back

Linear

Front

Identify the function type: y = x^2 - 4

Back

Nonlinear

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

What does the y-intercept (b) represent in a linear function?

Back

The y-intercept (b) is the value of y when x is 0; it is the point where the line crosses the y-axis.

Front

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

Back

Nonlinear

Front

Identify the function type: y = -5x + 10

Back

Linear

Front

What is the graph of a linear function?

Back

The graph of a linear function is a straight line.