Linear vs Nonlinear Functions

Front

What is a function?

Back

A relation where each input (x-value) has exactly one output (y-value).

Front

How can you tell if a relation is not a function?

Back

If any x-value is paired with more than one y-value.

Front

What is a linear function?

Back

A function that graphs to a straight line, having a constant rate of change.

Front

What is a nonlinear function?

Back

A function that does not graph to a straight line, showing a variable rate of change.

Front

What does it mean for a table to represent a linear function?

Back

The differences between consecutive y-values are constant for equal differences in x-values.

Front

What does it mean for a table to represent a nonlinear function?

Back

The differences between consecutive y-values are not constant for equal differences in x-values.

Front

How can you determine if a graph represents a linear function?

Back

If the graph forms a straight line.

Front

How can you determine if a graph represents a nonlinear function?

Back

If the graph curves or does not form a straight line.

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function; if a vertical line crosses the graph more than once, it is not a function.

Front

What is the slope of a linear function?

Back

The rate of change, calculated as the rise over run between two points on the line.