The Power of Absolute Value Function: Understanding its Properties and Applications in Calculus and Linear Algebra

Absolute Value Function

f(x)=|x|

The absolute value function is a mathematical function that returns the absolute value of a number, which is its distance from zero on the number line. The absolute value function is denoted by two vertical bars surrounding the number, such as |x|. Here are some key points to keep in mind about absolute value:

1. The absolute value of a number is always positive or zero.
2. For example, the absolute value of 5 is 5, and the absolute value of -5 is also 5.
3. The absolute value function is symmetrical around the y-axis.
4. If you graph the absolute value function, it will look like a V-shape with its tip at the origin.
5. The absolute value of a number can be expressed as a piecewise function:

|x| = x if x >= 0
|x| = -x if x < 0 6. The absolute value function is used to measure the distance between two points on a number line or in a coordinate plane. 7. It is also used in a wide range of mathematical concepts, from calculus to linear algebra. For example, in calculus, the absolute value function is used to calculate limits, derivatives, and integrals of certain functions.

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