Linear vs. Nonlinear Tables and Graphs

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, characterized by a constant rate of change.

Front

What is the definition of a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed, indicating that the rate of change is not constant.

Front

How can you identify a linear function from its equation?

Back

A linear function can be identified by its equation in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the value of y when x is zero.

Front

What is a common characteristic of nonlinear functions?

Back

Nonlinear functions often exhibit curves or bends in their graphs, indicating varying rates of change.

Front

How do you determine if a graph is linear or nonlinear?

Back

A graph is linear if it forms a straight line; it is nonlinear if it curves or has bends.

Front

What is the relationship between initial value and slope in linear functions?

Back

In linear functions, the initial value is represented by the y-intercept, while the slope indicates the rate of change from that initial value.

Front

What does it mean for a function to have a constant rate of change?

Back

A constant rate of change means that the change in the output (y) is proportional to the change in the input (x) across the entire domain of the function.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which indicates that as x increases, y decreases.