We discuss how to compute absolute values, as well as some techniques to speed up the process.

Computing absolute value functions is a relatively straightforward process, but it can be a bit arcane if you haven’t seen it before, so we cover it in brief here.

Lecture Video

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Text and details

When computing values or functions that involve absolute values, you want to treat the absolute values like parentheses - essentially terms that are sealed off from other and must be computed separately before the inside values can interact with any of the outside values. Unlike parentheses however, there is no distribution rules that allow us to remove the absolute values without computing them first.

Take, for example, the function . To compute we would plug in for each to get

At this point we know that the absolute value “makes the value positive”. The we can simply replace the with , although technically the absolute value accomplishes this by multiplying the negative number inside by . Either way we end up with:

So, computing absolute values means that we have to compute the inside of the absolute value first, down to a value we can identify as positive or negative, so we can evaluate the absolute value part itself - forcing the output to be positive, before we move on with the rest of the expression.