Q61. - Algebra 1

Question

Explain why an absolute value can never be negative.

Step-by-Step Solution

Answer

The absolute value is used to tell about the distance and ignores the direction. As the direction is not considered, the absolute value can only be zero or any positive number.

Step-1. Consider absolute value function f(x).

Let a function $f\left(x\right)=\left|x\right|$ which represents an absolute value function.

Step-2. Explanation for absolute value function.

The absolute value is used to tell about the distance and ignores the direction.

As the direction is not considered, the absolute value can only be zero or any positive number.

Therefore, for the considered function $f\left(x\right)=\left|x\right|$ the absolute value function can be written as:

$\begin{array}{l}f\left(x\right)=\left|x\right|\\ \text{or }f\left(x\right)=\left(\begin{array}{c}x\text{if }x\ge 0\\ -x\text{if }x<0\end{array}\right)\end{array}$

Step-3. Reason for the absolute value function to be either positive or zero.

The absolute value is used to tell about the distance and ignores the direction.

As the direction is not considered, the absolute value can only be zero or any positive number.