Intervals of a Function

Front

What is an increasing interval of a function?

Back

An increasing interval is a range of x-values where the function's output (y-values) rises as x increases.

Front

What is a decreasing interval of a function?

Back

A decreasing interval is a range of x-values where the function's output (y-values) falls as x increases.

Front

What is a constant interval of a function?

Back

A constant interval is a range of x-values where the function's output (y-values) remains the same as x increases.

Front

How do you identify increasing intervals on a graph?

Back

Increasing intervals can be identified where the graph slopes upwards from left to right.

Front

How do you identify decreasing intervals on a graph?

Back

Decreasing intervals can be identified where the graph slopes downwards from left to right.

Front

How do you identify constant intervals on a graph?

Back

Constant intervals can be identified where the graph is horizontal, indicating no change in y-values.

Front

What does the notation [a, b] signify in interval notation?

Back

The notation [a, b] signifies that the interval includes both endpoints a and b.

Front

What does the notation (a, b) signify in interval notation?

Back

The notation (a, b) signifies that the interval does not include the endpoints a and b.

Front

What is the significance of endpoints in interval notation?

Back

Endpoints indicate whether the values at those points are included (closed interval) or excluded (open interval) in the interval.

Front

How can you determine the overall behavior of a function from its intervals?

Back

By analyzing the intervals of increase, decrease, and constancy, you can determine the overall behavior and trends of the function.