3.5 ESL Flashcard

Front

What is a Linear Function?

Back

Front

What is a Nonlinear Function?

Back

A nonlinear function is a function that does not graph to a straight line. Its graph can be a curve or any shape that is not a straight line.

Front

What does it mean for a function to be Increasing?

Back

A function is increasing on an interval if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be Decreasing?

Back

A function is decreasing on an interval if, as the input values increase, the output values decrease.

Front

What does it mean for a function to be Constant?

Back

A function is constant on an interval if the output values do not change as the input values change.

Front

How can you determine if a function is Linear or Nonlinear from its graph?

Back

If the graph is a straight line, the function is linear. If the graph is curved or has any shape other than a straight line, the function is nonlinear.

Front

What is the significance of the slope in a linear function?

Back

The slope (m) indicates the steepness of the line and the direction of the function. A positive slope means the function is increasing, while a negative slope means it is decreasing.

Front

What is an interval in the context of functions?

Back

An interval is a range of input values (x-values) over which a function is analyzed for its behavior, such as increasing, decreasing, or constant.

Front

What does it mean for a function to be 'never decreasing'?

Back

A function is 'never decreasing' if it either increases or remains constant over its entire domain.

Front

What is the difference between a function that is 'increasing' and one that is 'both increasing and decreasing'?

Back

An increasing function consistently rises, while a function that is both increasing and decreasing has sections where it rises and sections where it falls.