Intervals of a Function

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 x1 and x2 in the interval, if x1 < x2 then f(x1) < f(x2).

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 x1 and x2 in the interval, if x1 < x2 then f(x1) > f(x2).

Front

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

Back

A function is constant on an interval if, for any two points x1 and x2 in the interval, f(x1) = f(x2).

Front

How do you denote an interval that includes its endpoints?

Back

An interval that includes its endpoints is denoted using square brackets, e.g., [a, b].

Front

How do you denote an interval that does not include its endpoints?

Back

An interval that does not include its endpoints is denoted using parentheses, e.g., (a, b).

Front

What is the interval notation for all real numbers less than 6?

Back

(-∞, 6).

Front

What is the interval notation for all real numbers greater than or equal to -5?

Back

[-5, ∞).

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include endpoints (e.g., (a, b)), while closed intervals do include endpoints (e.g., [a, b]).

Front

How can you determine where a function is negative?

Back

A function is negative on an interval if f(x) < 0 for all x in that interval.