Intervals of Functions

Front

What is an interval in mathematics?

Back

An interval is a set of real numbers that contains all numbers between any two numbers in the set.

Front

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

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than at the first point.

Front

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

Back

A function is decreasing on an interval if, for any two points in that interval, the function's value at the second point is less than at the first point.

Front

What is a positive interval?

Back

A positive interval is where the function's values are greater than zero.

Front

What is a negative interval?

Back

A negative interval is where the function's values are less than zero.

Front

How do you denote an open interval?

Back

An open interval is denoted using parentheses, e.g., (a, b), meaning it does not include the endpoints a and b.

Front

How do you denote a closed interval?

Back

A closed interval is denoted using brackets, e.g., [a, b], meaning it includes the endpoints a and b.

Front

What is the significance of the interval notation (1, ∞)?

Back

The interval (1, ∞) includes all real numbers greater than 1, extending indefinitely.

Front

What does the interval (-∞, -2) represent?

Back

The interval (-∞, -2) includes all real numbers less than -2.

Front

How can you determine where a function is positive?

Back

To determine where a function is positive, find the intervals where the function's output is greater than zero.