Positive and Negative Intervals

In mathematics, an interval is a set of real numbers between two endpoints. Intervals can be classified as either positive or negative depending on the sign of the numbers in the interval.

Table of Contents:

• Positive and Negative Intervals
• Formula to determine the sign of an interval
• Solved Examples for Positive Intervals
• Solved Examples for Negative Intervals
• FAQs

Positive and Negative Intervals

A positive interval is an interval that contains only positive numbers. For example, the interval (0, 5) is a positive interval because all the numbers between 0 and 5 are positive.

A negative interval is an interval that contains only negative numbers. For example, the interval (-10, -5) is a negative interval because all the numbers between -10 and -5 are negative.

It’s also possible to have intervals that contain both positive and negative numbers. For example, the interval (-3, 3) contains both positive and negative numbers.

To determine the sign of an interval, you can look at the signs of the endpoints. If both endpoints are positive, then the interval is positive. If both endpoints are negative, then the interval is negative. If one endpoint is positive and the other is negative, then the interval contains both positive and negative numbers.

Intervals are commonly used in algebra and calculus to represent ranges of values for functions and to describe the behavior of functions over certain ranges.

Formula to determine the sign of an interval

The formula to determine the sign of an interval is as follows:

If both endpoints of the interval are positive, then the interval is positive. If both endpoints are negative, then the interval is negative. If one endpoint is positive and the other is negative, then the interval contains both positive and negative numbers.

In other words, if we have an interval of the form (a, b), where a and b are real numbers, we can determine its sign as follows:

If a > 0 and b > 0, then the interval is positive.
If a < 0 and b < 0, then the interval is negative.
If a < 0 and b > 0, then the interval contains both positive and negative numbers.
For example, the interval (-3, 5) contains both negative and positive numbers, so it is neither a positive nor a negative interval. On the other hand, the interval (-1, -0.5) contains only negative numbers, so it is a negative interval. Similarly, the interval (2, 8) contains only positive numbers, so it is a positive interval.

Solved examples for Positive Intervals

(0, 10) – This interval contains all positive numbers between 0 and 10, but does not include 0 or 10.

(1, ∞) – This interval contains all positive numbers greater than 1. The symbol ∞ represents infinity, so the interval continues indefinitely in the positive direction.

(2, 5) – This interval contains all positive numbers between 2 and 5, but does not include 2 or 5.

(0.1, 1) – This interval contains all positive numbers between 0.1 and 1, but does not include 0.1 or 1.

To represent these intervals on a number line, we would draw a line with a tick mark at 0, a tick mark at 10 (for example), and tick marks at any other endpoints, and then shade in the portion of the line that corresponds to the interval.

For example, to represent the interval (0, 10) on a number line, we would draw a line with a tick mark at 0 and a tick mark at 10, and then shade in the portion of the line between these two points.

Solved examples for Negative Intervals

(-10, 0) – This interval contains all negative numbers between -10 and 0, but does not include -10 or 0.

(-∞, -1) – This interval contains all negative numbers less than -1. The symbol ∞ represents infinity, so the interval continues indefinitely in the negative direction.

(-5, -2) – This interval contains all negative numbers between -5 and -2, but does not include -5 or -2.

(-1, -0.1) – This interval contains all negative numbers between -1 and -0.1, but does not include -1 or -0.1.

To represent these intervals on a number line, we would draw a line with a tick mark at 0, a tick mark at -10 (for example), and tick marks at any other endpoints, and then shade in the portion of the line that corresponds to the interval.

For example, to represent the interval (-10, 0) on a number line, we would draw a line with a tick mark at -10 and a tick mark at 0, and then shade in the portion of the line between these two points.

Positive and Negative Intervals FAQS

Grade 8 Science Worksheets

• Earth & Space Science
• Physical Science
• Life Science
• Chemistry
• Structure of Atom (Basic)
• Fossils
• Bio Classification
• Sedimentary Rock
• Chemical Reaction
• Climate
• Compounds and Mixtures
• The Universe
• Dynamics of our solar system
• Organization of the universe, and its development
• Earth Systems
• Rocks and Fossils
• Sources of energy that power the subsystems and cycles of the dynamic earth: the geosphere, hydrosphere, atmosphere and biosphere
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• Behavior of animals
• Understanding biological evolution
• How Living things are classified
• How Living Systems live
• Life Cycle of living things
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• States and properties of matter
• Changes in States Of Matter
• Chemical properties of Matter
• Structure of matter
• Conservation of matter
• Basics of chemical reactions
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• Laws and Formulas Of Motion

Grade 8 Math Worksheets

• Rational & Irrational Numbers
• Prime Factorization
• Comparing Inetgers
• Exponent Rules
• Ratios and Proportions
• Permutations and Combinations
• Scientific Notation
• Linear Functions
• Percents
• Variable Expressions