delimiter size in cases environment

Question

How can I change delimiter (brace) size in cases environment (for piece-wise function)?

\begin{equation}
f(x)=\begin{cases}

\end{cases}
\end{equation}

Answer 1

If the size of the brace (vertical and/or horizontal) are of prime concern, an alternative to the cases environment is given below. In this MWE, the stacked cases are composed of a \Vectorstack (stackengine package) in which the argument is set in math mode on equally spaced lines set about the math axis. The brace is produced by the scalerel package, and is merely a width-limited vertical scale of a glyph, in this case the left brace {.

\documentclass{article}
\usepackage[usestackEOL]{stackengine}
\usepackage{scalerel}
\begin{document}
\centering
Vertical height of brace matches target stack:
\[ f(x) =
  \scalerel[2ex]{\{}{\Vectorstack{a\\b\\c}}
\]
\[ f(x) =
  \scalerel[2ex]{\{}{\Vectorstack{a\\b\\c\\d}}
\]
Vertical height of stack can be extended beyond stack height:
\[ f(x) =
  \scalerel[2ex]{\{}{\addstackgap[3pt]{\Vectorstack{a\\b\\c\\d}}}
\]
Maximum horizontal width of brace set by optional parameter:
\[ f(x) =
  \scalerel[3ex]{\{}{\Vectorstack{a\\b\\c\\d}}
\]
\[ f(x) =
  \scalerel[4ex]{\{}{\Vectorstack{a\\b\\c\\d}}
\]
\[ f(x) =
  \scalerel[1ex]{\{}{\Vectorstack{a\\b\\c\\d}}
\]
\end{document}

This is just a demonstration of the ability to manipulate the brace. For a real problem, there may be other considerations... If the vertical separation between "cases" needs to be increased, \setstackgap{L}{length} prior to the stack can accomplish that, for example. See the package documentations for details. Your mileage may vary.