How to typeset piecewise-defined functions? [duplicate]

Question

I am attempting to write out the basic process for finding the absolute value of some number.

In ASCII, this is what I am attempting to write.

|X| = {
        x  if x > 0
        0  if x = 0
        -x if x < 0
      }

This is what I have so far.

\begin{equation}
\left|x\right| = \biggl\{ x\ if\ x > 0 \biggr\}
\end{equation}

I cannot figure out how to add the vertical spacing to allow the other two lines.

Answer 1

Option 1 (recommended)

left aligned

\documentclass[preview,border=12pt,varwidth]{standalone}
\usepackage{mathtools}
\begin{document}
\abovedisplayskip=0pt\relax
\[
\lvert x \rvert =
\begin{cases}
x & \text{if } x>0\\
0 & \text{if } x=0\\
-x& \text{if } x<0
\end{cases}
\]
\end{document}

Option 2 (just for fun)

right aligned

\documentclass[preview,border=12pt,varwidth]{standalone}
\usepackage{mathtools}
\begin{document}
\abovedisplayskip=0pt\relax
\[
\lvert x \rvert =
\left\{
\!
\begin{aligned}
x & \text{ if } x>0\\
0 & \text{ if } x=0\\
-x& \text{ if } x<0
\end{aligned}
\right.
\]
\end{document}

Important Notes

standalone class and \abovedisplayskip=0pt are settings for my own purpose to create a standalone and tight output. You should not use it for your production unless your objective is the same as mine.

Answer 2

Using the beta version of my tabstackengine package presented at Writing a table with equally spaced columns, based on the widest column, I can give you a number of configurable options on the appearance of the output. First, I give it with the package default spacings. Then I show how the horizontal gap can be increased in the stack, and finally how the interline spacing can be increased.

\documentclass{article}
\usepackage{tabstackengine}
\begin{document}
\[
\vert X\vert = \left\{
\alignVectorstack{
&x &\mathrm{if~} & x > 0\\
&0 &\mathrm{if~} & x = 0\\
&-x&\mathrm{if~} & x < 0
}
\right.
\]
\setstackaligngap{3em}
\[
\vert X\vert = \left\{
\alignVectorstack{
&x &\mathrm{if~} & x > 0\\
&0 &\mathrm{if~} & x = 0\\
&-x&\mathrm{if~} & x < 0
}
\right.
\]
\setstackgap{L}{1.4\baselineskip}
\[
\vert X\vert = \left\{
\alignVectorstack{
&x &\mathrm{if~} & x > 0\\
&0 &\mathrm{if~} & x = 0\\
&-x&\mathrm{if~} & x < 0
}
\right.
\]
\end{document}