Positive/Negative and Increasing/Decreasing Intervals

Front

What is a positive interval in a function?

Back

A positive interval is a range of x-values where the function's output (y-values) is greater than zero.

Front

Define a negative interval in a function.

Back

A negative interval is a range of x-values where the function's output (y-values) is less than zero.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the value of the function also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the value of the function decreases.

Front

How do you identify increasing intervals on a graph?

Back

Increasing intervals can be identified where the graph of the function rises as you move from left to right.

Front

How do you identify decreasing intervals on a graph?

Back

Decreasing intervals can be identified where the graph of the function falls as you move from left to right.

Front

What is the notation for an interval?

Back

Intervals are typically denoted using parentheses ( ) for open intervals and brackets [ ] for closed intervals.

Front

What is an open interval?

Back

An open interval (a, b) includes all numbers between a and b but does not include a and b themselves.

Front

What is a closed interval?

Back

A closed interval [a, b] includes all numbers between a and b, including a and b themselves.

Front

How do you find the positive intervals of a function?

Back

To find positive intervals, identify the ranges of x-values where the function's output is greater than zero.