Absolute Value Function
The absolute value function is a mathematical function that gives the distance between a given number and zero on a number line
The absolute value function is a mathematical function that gives the distance between a given number and zero on a number line. It is denoted by two vertical bars surrounding the number, such as |x|. The absolute value of a number is always positive or zero.
The absolute value function can be defined as follows:
For any real number x, the absolute value of x, denoted as |x|, is defined as:
– |x| = x, if x is greater than or equal to zero
– |x| = -x, if x is less than zero
To understand this definition, let’s consider a few examples.
Example 1:
Given the number x = 5, to find the absolute value of x, we look at the definition.
Since x is greater than or equal to zero, we have |5| = 5.
So, the absolute value of 5 is 5.
Example 2:
Now, let’s consider the number x = -3.
Using the definition again, since x is less than zero, we have |(-3)| = -(-3) = 3.
So, the absolute value of -3 is 3.
Example 3:
Finally, let’s consider x = 0.
Since 0 is equal to zero, we use the first part of the definition which states that |0| = 0.
So, the absolute value of 0 is 0.
In summary, the absolute value function gives us the positive distance between a number and zero on the number line. It is defined as |x| = x, if x is greater than or equal to zero, and |x| = -x, if x is less than zero.
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