# Interval Notation Calculator

The interval notation calculator is a free online tool that displays the number line for the interval input. Our interval notation calculator tool is an online tool that makes calculations faster and shows the number line in a fraction of a second.

## How to Use the Interval Notation Calculator?

To use the interval notation calculator, follow these steps:

Step 1: Fill out the input fields with the interval (closed or open)

Step 2: Click the Calculate button to obtain the results

Step 3: Once the new window is opened, the number line representing the given interval will be displayed

## What Is An Interval In Mathematics?

A mathematical interval is a set of real numbers that falls between two given numbers called the endpoints of the interval. The set contains all the numbers lying between the two endpoints of the set. They may or may not be included in the set, depending on the interval’s “type” or notation.

Before we discuss these notations, let’s look at an example of an interval: the set of numbers x satisfying -1 ≤ x ≤ 1 is an interval that includes -1, 1, and all the numbers between them. In our example, the interval could have included the endpoints, but not in our example. Therefore, the interval would be -1 < x < 1. As a result, the interval only contains zeroes and ones within the range. The real intervals play an important role in integration theory because their “size” or “measure” is the simplest and easiest to define.

• Inequalities
• Interval Notation
• The Number Line

### Inequalities

With Inequalities we use:

• > greater than
• ≥ greater than or equal to
• < less than
• ≤ less than or equal to

Like this:

Example: x ≤ 20
Says: “x less than or equal to 20”

And means: up to and including 20

### Interval Notation

In “Interval Notation” we just write the beginning and ending numbers of the interval, and use:

• [ ] a square bracket when we want to include the end value, or
• ( ) a round bracket when we don’t

Like this:

Example: (5, 12]

From 5 to 12, do not include 5 but do include 12

Depending on the characteristics of their two endpoints (a and b), intervals are notated in different ways, known as interval notation. Including a and b, we note the interval as [a,b], and excluding a and b, we note the interval as (a,b). For countries that use commas to write decimal numbers, we can replace the comma with a semicolon.

The Symbol for Interval Notation

The notations we use for different intervals are:

• [ ]: Square brackets are used when both endpoints are in the set.
• ( ): The round bracket is used when both endpoints are excluded.
• ( ]: This is a semi-open bracket that excludes the left endpoint, while the right endpoint is included in the set.
• [ ): The left endpoint of this bracket is also included, while the right endpoint is excluded.

An open interval

An open interval with endpoints a and b does not include the endpoints in the interval. This means that the interval ]a,b[ is formed by all the numbers of the interval that are found between a and b. Formally, we will write that x belongs to the interval if a<x<b.

Graphically, an open gap is represented by a segment whose ends are formed by hollowed-out points.

To write this interval in interval notation, you must use parentheses: (a,b).

A half-open interval

Semi-open intervals can also be semi-closed, which is what we call half-open intervals. Intervals with no endpoints include only one of them in the interval. Right or left, a semi-open interval exists.

]a,b] includes all the numbers either greater than a or less or equal to b regarding the endpoints of the interval to the left. The interval contains x if a < x ≤ b. Semi-open intervals are represented graphically by segments whose left end is hollowed out and the right end is solid.

A half-open interval to the right with endpoints a and b [a,b[ includes all the numbers greater than or equal to a and strictly less than b. We will write that x belongs to this interval if a ≤ x < b. Half-open intervals on the right are represented graphically by segments with solid left ends and recessed right ends.

Use parentheses to show whether an endpoint is included or excluded from this interval, and square brackets to show whether it is included (a,b]; use parentheses to show whether it is excluded [a,b).

A closed interval

A closed interval with endpoints a and b includes both of them in the interval. Meaning that the interval [a,b] is formed by all the numbers between a and b. We write that x belongs to the interval if a ≤ x ≤ b. Graphically, a closed interval is represented by a segment whose two ends are filled.

To write this interval in interval notation, you must use square brackets: [a,b].

### Number Line

With the Number Line we draw a thick line to show the values we are including, and:

• a filled-in circle when we want to include the end value, or
• an open circle when we don’t

Look at the handy table that distinguishes between all the types of intervals.

## How To Convert Inequality To Interval Notation?

Follow the steps mentioned below to convert an inequality to interval notation.

• Graph the solution set of the interval on a number line.
• Write the numbers in the interval notation with a smaller number appearing first on the number line on the left.
• If the set is unbounded on the left, use the symbol −∞ and if it is unbounded on right, use the symbol ∞.

Let’s take a few examples of inequality and convert them to interval notation.

## Important Points To Remember

• Interval notation is used to express the set of inequalities.
• There are 3 types of interval notation: open interval, closed interval, and half-open interval.
• The interval with no infinity symbol is called a bounded interval.
• The interval containing the infinity symbol is called an unbounded interval.

## Inequality to Interval Notation Calculator:

An inequality to interval notation calculator is a tool that converts an inequality into its equivalent interval notation. Interval notation represents a range of values on the number line. For example, the inequality “x > 2” can be expressed in interval notation as (2, ∞), where the parentheses indicate that 2 is not included in the interval and the symbol “∞” represents infinity.

Example:
Let’s say we have the inequality 3 ≤ x < 7. Using the inequality to interval notation calculator, we can convert it to the interval notation [3, 7), where the square bracket indicates that both 3 and 7 are included in the interval, and the parenthesis indicates that 7 is not included.

Solution:
To convert an inequality to interval notation, follow these steps:
1. Identify the inequality symbol (>, <, ≥, or ≤).
2. Determine if the inequality includes or excludes the endpoints.
3. Write the lower bound and upper bound of the interval using parentheses or square brackets.

## Domain Interval Notation Calculator:

A domain interval notation calculator is a tool used to determine the domain of a function and represent it in interval notation. The domain of a function is the set of all possible input values or x-values for which the function is defined. Interval notation provides a concise and clear representation of the domain.

Example:
Consider the function f(x) = √(x – 3). The domain of this function would exclude any values of x that would result in a negative number under the square root, as the square root of a negative number is undefined in the real number system. Therefore, using the domain interval notation calculator, we can express the domain of the function as (-∞, 3].

Solution:
To find the domain of a function and represent it in interval notation, follow these steps:
1. Identify any restrictions or conditions that could limit the domain.
2. Determine the intervals or values for which the function is defined.
3. Express the domain using interval notation.

## Interval Notation Graph Calculator:

An interval notation graph calculator is a tool that helps visualize and represent intervals on a graph. It allows you to input the interval notation and generate a graph that shows the corresponding range of values on the number line.

Example:
Suppose we have the interval notation (2, 5) and want to visualize it on a graph. Using the interval notation graph calculator, we would see a graph with an open circle at 2 and an open circle at 5, indicating that both endpoints are excluded from the interval. The line segment between the two circles represents all the values within the interval.

Solution:
To use an interval notation graph calculator, follow these steps:
1. Input the interval notation you want to graph.
2. Review the generated graph, which typically includes circles or dots to represent open or closed endpoints and a line segment connecting them.

## Interval Notation Domain Calculator:

An interval notation domain calculator is a tool that determines the domain of a function or set of values and expresses it in interval notation. It helps identify the valid input values for a function or set of values.

Example:
Consider the function g(x) = 1/(x – 2). The domain of this function would exclude x = 2 since dividing by zero is undefined. Using the interval notation domain calculator, we can represent the domain of the function as (-∞, 2) U (2, ∞), where the “U” symbol denotes the union of two intervals.

Solution:
To find the domain of a function or set of values and represent it in interval notation, follow these steps:
1. Identify any restrictions or conditions that could limit the domain.
2. Determine the intervals or values for which the function or set is defined.
3. Express the domain using interval notation and the union symbol if there are multiple intervals.

## Interval Notation Calculator With Steps:

An interval notation calculator with steps is a tool that not only provides the result in interval notation but also shows the step-by-step process of how the conversion or calculation was done. This helps users understand the reasoning behind the conversion and verify the accuracy of the result.

Example:
Suppose we have the inequality -3 ≤ 2x + 1 < 7 and want to convert it to interval notation. Using an interval notation calculator with steps, we would see the following:
-3 ≤ 2x + 1 < 7
-4 ≤ 2x < 6
-2 ≤ x < 3
The steps show the transformation of the original inequality to the final interval notation result.

Solution:
To use an interval notation calculator with steps, follow these steps:
1. Input the expression or inequality you want to convert or calculate.
2. Review the generated steps, which should provide a clear breakdown of the process involved in the conversion or calculation.

## How to Find Interval Notation:

Finding interval notation involves determining the lower and upper bounds of a range of values and expressing them in a concise notation. Interval notation is commonly used to represent intervals on the number line.

Example:
Let’s say we have the range of values from -5 to 3, including both endpoints. To find the interval notation for this range, we write it as [-5, 3], using square brackets to indicate that both -5 and 3 are included in the interval.

Solution:
To find interval notation, follow these steps:
1. Identify the lower bound and upper bound of the range.
2. Determine if the endpoints are included or excluded.
3. Express the interval using parentheses or square brackets, depending on whether the endpoints are included or excluded.

## Union Interval Notation Calculator:

A union interval notation calculator is a tool that combines or merges multiple intervals into a single representation using the union symbol “U.” This is useful when dealing with functions or sets that have multiple intervals in their domain or range.

Example:
Suppose we have two intervals: (1, 4) and [6, 9). Using the union interval notation calculator, we can express the union of these intervals as (1, 4) U [6, 9), indicating that the values from both intervals are included in the overall set.

Solution:
To use a union interval notation calculator, follow these steps:
1. Input the intervals you want to combine.
2. Review the generated result, which should show the union of the intervals using the “U” symbol.

## Conclusion

The article focused on the fascinating concept of interval notation. The students begin by applying what they already know about Interval Notation, and then creatively frame a novel concept in their minds. The message must be relevant, easy to understand, and stick with them for a lifetime.

What is interval notation on a graph?

When we represent the solution set of an interval on a number line, that is a graph for the interval notation.

What is the ∪ symbol for interval notation?

The ∪ symbol is used to denote the union of two or more intervals.

How do you exclude numbers in interval notation?

We use the round brackets to exclude numbers in interval notation.

How To Convert Inequality To Interval Notation Calculator?

To convert an inequality to interval notation, you can follow these steps:

Step 1: Identify the inequality symbol: Determine whether the inequality symbol is “<“, “>”, “<=”, or “>=”.

Step 2: Determine the inclusion or exclusion of endpoints: Determine if the endpoints of the interval are included or excluded. This depends on whether the inequality uses a strict inequality symbol (“<” or “>”) or an inclusive inequality symbol (“<=” or “>=”).

Step 3: Write the interval notation: Based on the inequality symbol and inclusion/exclusion of endpoints, write the interval notation. Use square brackets “[]” to indicate inclusive endpoints and parentheses “()” to indicate exclusive endpoints.

Here are a few examples to illustrate the process:

Example 1: Convert the inequality “x > 2” to interval notation.
– The inequality symbol is “>”.
– Since the symbol is “>”, the endpoint 2 is excluded.
– The interval notation for the inequality “x > 2” is (2, ∞), where ∞ represents infinity.

Example 2: Convert the inequality “y ≤ -3” to interval notation.
– The inequality symbol is “≤”.
– Since the symbol is “≤”, the endpoint -3 is included.
– The interval notation for the inequality “y ≤ -3” is (-∞, -3].

What Is The Interval Notation For The Compound Inequality Calculator?

The interval notation for a compound inequality can be determined by combining the individual interval notations for each part of the compound inequality using the appropriate logical operator (AND or OR).

For example, if we have the compound inequality “x > 2 AND x ≤ 5,” we can break it down into two separate inequalities: “x > 2” and “x ≤ 5”. We can then find the interval notation for each inequality and combine them using the logical operator “AND”.

Using the examples from the previous question:

– The interval notation for “x > 2” is (2, ∞).
– The interval notation for “x ≤ 5” is (-∞, 5].

To combine them, we use the logical operator “AND”, which means the values must satisfy both inequalities. Therefore, the interval notation for the compound inequality “x > 2 AND x ≤ 5” is (2, 5].

If the compound inequality used the logical operator “OR”, which means the values can satisfy either inequality, we would use the union symbol “U” instead. For example, if we had “x > 2 OR x ≤ 5”, the interval notation would be (2, ∞) U (-∞, 5].

How To Write Domain In Interval Notation From Function Calculator?

To write the domain of a function in interval notation, follow these steps:

Step 1: Identify any restrictions or conditions on the domain: Determine any values or conditions that would make the function undefined or result in an error. For example, square roots cannot be taken of negative numbers, so any values that would make the radicand negative should be excluded from the domain.

Step 2: Determine the intervals or values for which the function is defined: Identify the valid input values or x-values for the function.

Step 3: Write the domain using interval notation: Express the domain using interval notation, considering both inclusive and exclusive endpoints.

Here’s an example to illustrate the process:

Example: Consider the function f(x) = 1/(x – 2).
– The function is undefined when the denominator (x – 2) equals zero, so x = 2 is excluded from the domain.
– The function is defined for all other real numbers.
– Therefore, the

domain of f(x) in interval notation is (-∞, 2) U (2, ∞).

Where Is f(x) = 8x – 3 Continuous Interval Notation Calculator?

To determine the intervals where the function f(x) = 8x – 3 is continuous, we need to find the values of x for which the function is defined and does not have any breaks or discontinuities.

In this case, the function f(x) = 8x – 3 is a linear function, and linear functions are continuous over the entire real number line. Therefore, the function is continuous for all values of x.

In interval notation, we can represent the continuity of the function as (-∞, ∞), indicating that the function is continuous for all real numbers.

How Do You Find Interval Notation?

To find interval notation, follow these general steps:

Step 1: Identify the lower and upper bounds: Determine the minimum and maximum values of the interval.

Step 2: Determine the inclusion or exclusion of endpoints: Determine whether the interval includes or excludes the lower and upper bounds. Use square brackets “[]” to indicate inclusive endpoints and parentheses “()” to indicate exclusive endpoints.

Step 3: Write the interval notation: Based on the lower and upper bounds and inclusion/exclusion of endpoints, write the interval notation using the appropriate notation symbols.

For example, if the lower bound is 3 (inclusive) and the upper bound is 7 (exclusive), the interval notation would be [3, 7). If the lower bound is -∞ (negative infinity) and the upper bound is 4 (exclusive), the interval notation would be (-∞, 4).

How Do You Write Interval Notation Examples?

To write interval notation examples, you need to consider the lower and upper bounds of the interval and the inclusion or exclusion of endpoints. Here are a few examples:

Example 1: The interval from -2 to 5, including both endpoints:
– Lower bound: -2 (inclusive)
– Upper bound: 5 (inclusive)
– Interval notation: [-2, 5]

Example 2: The interval from 0 to 10, excluding the lower bound:
– Lower bound: 0 (exclusive)
– Upper bound: 10 (inclusive)
– Interval notation: (0, 10]

Example 3: The interval from -∞ to 3, including the upper bound:
– Lower bound: -∞ (negative infinity)
– Upper bound: 3 (inclusive)
– Interval notation: (-∞, 3]

Example 4: The interval from 1 to 6, excluding both endpoints:
– Lower bound: 1 (exclusive)
– Upper bound: 6 (exclusive)
– Interval notation: (1, 6)

Remember to use square brackets “[]” for inclusive endpoints and parentheses “()” for exclusive endpoints.

How Do You Convert A Set To Interval Notation?

To convert a set to interval notation, follow these steps:

Step 1: Identify the lower and upper bounds of the set: Determine the minimum and maximum values within the set.

Step 2: Determine the inclusion or exclusion of endpoints: Determine whether the set includes or excludes the lower and upper bounds. Use square brackets “[]” to indicate inclusive endpoints and parentheses “()” to indicate exclusive endpoints.

Step 3: Write the interval notation: Based on the lower and upper bounds and inclusion/exclusion of endpoints, write the interval notation using the appropriate notation symbols.

Here’s an example to illustrate the process:

Example: Convert the set {x | -3 ≤ x < 5} to interval notation.
– The lower bound is -3 (inclusive), and the upper bound is 5 (exclusive).
– The set includes -3 but does not include 5.
– The interval notation for the set {x | -3 ≤ x < 5} is [-3, 5).

Remember that the interval notation represents a range of values, and the endpoints can be inclusive or exclusive based on the conditions of the set.