Absolute value functions

When were told about absolute value, one thing comes in mind, it’s that it will never be a negative value. It would always be positive. So if we are asked to give the absolute value of a negative number, we give a number that doesn’t have the negative sign. We were taught that absolute values are used to describe the distance of a number from zero. In real life, absolute values isn’t just used for that, it can be used in a variety of purposes, like distances. We never hear anyone say it’s -173 miles away from here, but rather we say it’s 173 miles from here.

In this chapter, we will look into absolute value, and absolute value functions. We have been discussing much about functions in the previous grade and chapters, and among the concepts that we need to learn about them is Absolute Value Function.

It is denoted by f(x) = |x|. It is often termed in mathematics as the piecewise function, f(x)= |x| = x, if x \geq 0 and –x if x < 0. We can readily solve them by using the given equation above, and check if we’re right by using an online absolute value calculator.

The domain of this function is the real numbers and the range are all the non-negative numbers.Absolute Value Functions are known to have a graph that is formed by two rays meeting at one point and forming a right angle in the vertex.

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Absolute value functions

Absolute value is basically the distance between “number” and “zero” on a number line. We will look into this concept in this lesson. We will also learn how to express absolute value functions as piecewise functions.


Definition of “Absolute Value”: | number | = distance between “ number ” and “zero”
  • 3.
    Express the absolute value function as a piecewise function: g(x)=54xg\left( x \right) = \left| {5 - 4x} \right|
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Absolute value functions

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