Define default option values for the function f:

Define f, allowing options to be given:

Use f with an explicit option setting:

Use f with options taken to have their default values:

Retrieve several option values at once:

Use an explicit list of options:

Define a transformation rule using multiple OptionsPattern constructs:

OptionValue[a] is treated as OptionValue[f,a] because it is the outer head:

OptionValue tracks where a particular option was specified:

Use Hold in the fourth argument to return the unevaluated forms of options using RuleDelayed:

Without the Hold, the current value of $Assumptions would be returned:

Define the default option values for a function f:

Implement f using a helper function fCore, but still inherit defaults from f:

The default option value of f is honored:

An explicit option setting takes precedence:

Define two functions with options:

Define a function h that uses both sets of options, giving preference to the defaults of g:

Contexts are ignored when comparing option names:

A string and a symbol are treated interchangeably:

OptionValue checks that all options requested appear in the defaults:

For simple cases, OptionValue[f,opts,name] is similar to name/.opts/.Options[f]:

However, OptionValue performs additional normalization to ensure rules are correctly applied: