In this absolute value calculator, we provide all of the necessary information about the absolute value function and its inequalities, and, obviously, we help you calculate the absolute value of any number. To help you understand better what an absolute value is, we have included some absolute value graphs and a few practical examples of solving absolute value equations. So come in and enjoy learning new things about absolute value! Show
🙋 Once you've mastered the absolute value of a number, you can go beyond and use our absolute value equation calculator. What is "absolute value"? – definitionLet's start from the beginning, shall we? The term absolute value might have different meanings, depending on the context, but here, in the mathematical world, it is very clearly defined. The absolute value definition is simply the value of the number, regardless of the sign. This absolute value definition is not the most technical one, but it's sure to confuse no one while explaining what absolute value is. For those who like more technicality when it comes to their mathematical definitions, we haven't forgotten about you:
Now that you know what absolute value is, we can talk about how to write it and operate with it in mathematical terms. The mathematical symbol for absolute value is To calculate the absolute value of a number, you simply "take the sign off" of the number. One can also think about it as "making the number inside positive." If you want to sound fancier, you can always make up your own way to explain, depending on what you'd like to compute. For example, "you find the distance between the number you're interested in and the value 0 (zero)". It is important to know that the absolute value operation is not just limited to numbers. It can be applied to expressions and equations like this: We will explain later how to calculate the absolute value of equations or the absolute value of a graph/function. For now, let's go step by step. Is absolute value useful?You bet it is! Oh! I guess you want some reasons and examples of what is absolute value useful for, right? Well, let's start with the easiest: any situation in which we care about differences and only differences. For example, when we are talking about the distance between two things. The obvious one is the distance between two points, which is, for example, necessary alongside time when calculating speed. For example, if a car starts at We can also use the absolute value as a way of abbreviating our writing. For example, if we want a function that gives only positive numbers, we could write a set of 'if...else' conditions, but that would get too long. This is where absolute value comes to the rescue: we can simply wrap our function inside the absolute value signs to give us permanent positive values. This means that Absolute value functions and absolute value graphsAnd this usefulness leads directly to absolute value graphs and absolute values inside of functions. Both are simple things in theory, but both are tricky in the beginning. Let's start with the most basic absolute value function: Digging a bit deeper, we can start with the positive part, Things get a bit more sophisticated when we get a more complicated expression inside the absolute value. As long as the absolute value surrounds the whole expression, we can use a small trick. If we look back at This same trick can be used for any absolute value function. Just draw the function ignoring the absolute value, and then flip over whatever part is below As a side note for those interested, any absolute value graph is as continuous as the non-absolute one, but will also have a sharp, non-differentiable point wherever the values have begun to change from positive to negative. For example, in the function For more complicated expressions where the absolute value function is inside the expression (like in Absolute value equations and absolute value inequalitiesA common place to find absolute values is when solving absolute value equations (or any kind of equation, really). Equations that have absolute values are known as absolute value equations; if instead of an equals ( The way to deal with absolute values in both cases is similar. When solving absolute value equations, you want to operate on and simplify things as much as possible while avoiding touching the absolute value part until you absolutely (pun intended) have to. Once we hit the point where we need to deal with the absolute value, we isolate it on one side of the sign and decompose it into its possible options: positives and negatives. This process is the same for both absolute value equations and absolute value inequalities. Let's see how that would look with a very simple example. Imagine you've managed to simplify everything to the point where you have the following equation:
We know that the part
while it is negative, the absolute value would change the sign, giving us the following:
Both equations represent potential solutions of the initial equation and would yield: a) Positive: If we pay close attention we can see that we are not done, since
which is a mathematical absurdity. This same process of dividing the absolute value equation or absolute value inequality, then checking what solutions make sense, is very useful and standard. You can use it when solving any absolute value equation (even if it's a quadratic formula), and your success is pretty much guaranteed. We used a very simple example here to keep it brief. Still, the same techniques can be used to solve very complex inequalities or find important points in absolute value functions so that you can draw the absolute value graphs we mentioned earlier. How to use the absolute value calculatorUsing the absolute value calculator is as easy as it gets. As a mathematical operation, the absolute value is very easy to find in and of itself, but we're going to try and talk you through a couple of tips that might help you. First of all, the absolute value calculator works by turning any number you input into a positive number, which is all the absolute value really is. So you should introduce a number in the input box of the calculator, and you will get its absolute value as a result. You can use this tool to check certain points of your absolute value graph and equation to make that sure your sketch, drawing, or solution is correct. It is a very simple calculator, and that is why we have provided all the information above: to turn this simple absolute value calculator into a tool to gain more knowledge, bound to be helpful in your life (or at least in your math class). How do you find the absolute value of a function?Absolute Value Functions. The absolute value parent function, written as f(x)=| x |, is defined as.. To translate the absolute value function f(x)=| x | vertically, you can use the function.. g(x)=f(x)+k.. To translate the absolute value function f(x)=| x | horizontally, you can use the function.. g(x)=f(x−h).. What is the range calculator?The Range Calculator is used to calculate the range value of a set of numbers.
What is the absolute value of |The absolute value of a negative number is also a positive value. If a number x < 0, then its absolute value is given by, |x| = -x. For example, |-2| = 2. Irrespective of the sign of the numeric value, the absolute value is always non-negative.
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