Increasing and Decreasing Intervals

Front

What is an increasing interval?

Back

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

Front

What is a decreasing interval?

Back

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

Front

What does it mean for a function to be constant on an interval?

Back

A function is constant on an interval if its output (y-values) does not change as x varies within that interval.

Front

How do you express the interval where a function is increasing in interval notation?

Back

Use parentheses for open intervals and brackets for closed intervals. For example, if a function is increasing from x = 1 to x = 3, it is expressed as (1, 3).

Front

How do you express the interval where a function is decreasing in interval notation?

Back

Use parentheses for open intervals and brackets for closed intervals. For example, if a function is decreasing from x = 2 to x = 5, it is expressed as (2, 5).

Front

What is the interval notation for -5 ≤ x < 8?

Back

The interval notation is [-5, 8).

Front

If a function is increasing on the interval (0, 3), what does this imply about its graph?

Back

The graph of the function rises as it moves from left to right between x = 0 and x = 3.

Front

What is the significance of critical points in determining increasing and decreasing intervals?

Back

Critical points are where the derivative is zero or undefined. They help identify where the function changes from increasing to decreasing or vice versa.

Front

How can you determine if a function is increasing or decreasing using its derivative?

Back

If the derivative of a function is positive on an interval, the function is increasing. If the derivative is negative, the function is decreasing.

Front

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

Back

The notation (a, b) represents an open interval where a and b are not included in the interval.