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 negative on an interval?

Back

A function is negative on an interval if its output values are less than zero for all inputs in that interval.

Front

How do you express the interval (a, b) in inequality notation?

Back

In inequality notation, (a, b) is expressed as a < x < b.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints, while closed intervals do include their endpoints.

Front

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

Back

A function is decreasing on an interval if, as the input values increase, the output values decrease.

Front

How do you represent the interval [-5, ∞) in set notation?

Back

In set notation, [-5, ∞) is represented as {x | x ≥ -5}.

Front

What is the interval notation for all real numbers?

Back

The interval notation for all real numbers is (-∞, ∞).

Front

How do you express the interval [3, 5) in inequality notation?

Back

In inequality notation, [3, 5) is expressed as 3 ≤ x < 5.

Front

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

Back

A function is positive on an interval if its output values are greater than zero for all inputs in that interval.

Front

How do you find the intervals where a function is positive or negative?

Back

To find intervals where a function is positive or negative, analyze the sign of the function's output over different intervals determined by its critical points.