LInear vs Nonlinear

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph and can be expressed in 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 equation cannot be written in the form y = mx + b.

Front

How can you tell if a table represents a function?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value). If any x-value is repeated with different y-values, it is not a function.

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 is the y-intercept (b) in a linear function?

Back

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

Front

What type of graph represents a linear function?

Back

A linear function is represented by a straight line on a graph.

Front

What type of graph represents a nonlinear function?

Back

A nonlinear function is represented by a curve or any shape that is not a straight line on a graph.

Front

Can a function be both linear and nonlinear?

Back

No, a function cannot be both linear and nonlinear. It is either one or the other based on its graph and equation.

Front

What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3.

Front

What is an example of a nonlinear function?

Back

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