Absolute Value
Table of Contents
Absolute Value
What does absolute value mean? Conceptually, the absolute value of a number is its distance from 0. Simplistically, it converts all numbers to a positive value.
Absolute Value Symbol
The absolute value symbol is two vertical lines next to a number |x|. The absolute value symbol is illustrated around 5 and -5 below and plotted on the number line below. Since both numbers are 5 places from zero, the absolute value is 5. A number line is a great method to show the distance from zero.
Absolute Value Equations
Absolute value equations can also have absolute values, see the following example. Even though the equation results in -4, the absolute value is 4 since -4 is 4 places from zero. The number line below illustrates how to solve absolute value equations.
Absolute Value Function
An absolute value function is a function inside absolute value symbols, typically shown as the following function. The x variable represents a real number and the absolute value symbol requires a non-negative value for that function.
Absolute Value Graph
Before we know how to create an absolute value graph, the absolute value parent function must be understood. There are different parent functions that can be graphed, the following is a simple example.
This simple function is a great way to demonstrate how to graph absolute value and the following table illustrates this. The table has inputs, outputs, and ordered pairs. Since y is equal to x, the function y = |x| results in all positive y values.
| Input (x) | Output (y) | Ordered Pair (x,y) |
| 7 | 7 | (7,7) |
| 3 | 3 | (3,3) |
| 0 | 0 | (0,0) |
| -3 | 3 | (-3,3) |
| -7 | 7 | (-7,7) |
Graphing absolute value functions is straightforward once the ordered pairs are understood. The ordered pairs are plotted on a graph and lines can be created.
Frequently Asked Questions
How to solve inequalities with absolute values?
Solving absolute value inequalities involves understanding a variable inside an absolute value equation may be positive or negative. This results in a positive and negative answer for each inequality with absolute values. The number lines in the following examples illustrate how this is possible.
What is the sum of absolute values?
In various problem types, it may be necessary to sum or add all the values in a dataset. To find the sum, all values must be converted to a positive number and added together.
What is the absolute value of -5?
The absolute value of -5 is 5. -5 has a distance of 5 from 0.
What is the absolute value of 0?
The absolute value of 0 is 0. This may be a tricky question because zero has no positive or negative value, but the distance from 0 is 0.
More Information
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