This is a high-level description of the model used in Function Builder. It's intended for audiences that are not necessarily technical.
Compared to other PhET simulations, the model in Function Builder is relatively simple. A set of zero or more functions is arranged in series in a function builder. The input to the builder is a set of cards that have something on them (call it the card's content). As you drag a card through the builder, the card's content is modified by functions. Intermediate results are visible through windows in the builder, that allow you to see what's happening inside the builder. The absence of a function is equivalent to the identity function.
In the Patterns screen, each card's content is an image. The functions are image transforms, which modify the image in various ways (rotation, scaling, color mapping, etc.)
In the other screens (Numbers, Equations, Mystery), each card's content is a number. The input cards display integers. The numeric functions are addition, subtraction, multiplication and division. Division by zero is not supported, and is specifically excluded by the simulation. The output cards display integers or mixed numbers (integer with proper fraction).
The Equations screen adds the symbol "x" on an input card. The same numeric functions are applicable to "x". The output in this case is an equation in slope-intercept form (y = mx + b). An additional equation format is also provided, as described in equation-formats.md.
In the Mystery screen, the objective is to guess the identity of a set of 1 or more functions. Each such set of functions is referred to as a challenge. The simulation has a set of predefined challenges, from which a challenge is selected at random. If you don't mind reading JavaScript code, you can view the sets of challenges in MysteryChallenges.
In all screens, the notion of non-invertible functions is supported. A function is not invertible if it's output cannot be run backwards through the function to produce the original input. Examples: Multiplication by zero is a non-invertible numeric function. Conversion to grayscale is a non-invertible image transform.
For invertible functions, the model in this simulation does not implement an explicit inverse function. Instead, all computation is performed in the forward direction, based on an input's location relative to a function. And a card's location is constrained based on whether a function is invertible; cards cannot be dragged backwards through non-invertible functions.