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← Jay, Kay & ElleAll games Function Factory

The Dollhouse family presents

Function Factory

Every machine follows a rule. Can you discover it?

INPUT→RULE→OUTPUT

Choose a workshop

Factory Stations

Finish Elle’s six opening investigations to unlock the full factory floor.

Challenges

Run the Machine

Elle

Let’s investigate what this machine does.

Input

Output

Machine record

Inputs and outputs tested in this machine
Input	Output

What comes out?

Ideas worth keeping

Factory Notebook

Save your mathematical work—not scores.

Import JSON

✎

Your first discovery can go here.

Save a challenge, an experiment, or a machine you build.

Factory field guide

How functions work

Input

The number that goes into a machine.

4→+ 3→7

Output

The number that comes out after the rule is followed.

Rule

The exact instructions a machine uses every time.

Test every row

A guessed rule must work for every example, not just the first one.

Run backward

Undo the last step first. “× 4, then + 3” runs backward as “− 3, then ÷ 4.”

Order matters

“× 2, then + 3” usually gives a different answer from “+ 3, then × 2.”

Graphs

Each plotted point is an input-output pair. Its horizontal position is the input x, and its vertical position is the output y.

Fractions

A function can make exact decimal or fractional outputs. You may enter either 0.75 or 3/4.

Nonlinear rules

Squaring and absolute value do not change at a constant rate. Compare negative and positive inputs to see their symmetry.

Ambiguity

A few examples may fit several rules. More evidence helps, but a pattern must be stated before it becomes a precise function rule.

Debugging

Run each input through the stated rule. The first row whose output disagrees contains a bug.

x, y, and f(x)

x names the input. y or f(x) names the output. So f(x) = 2x + 1 means “multiply the input by 2, then add 1.”

Factory controls

Settings

Sound effectsNo music. Sound starts only after you interact. Reduce motionFinish machine movements immediately.

All factory tools are open

Graphs, fractions, squaring, absolute value, ambiguity investigations, and function debugging are available from the station map, Explore, and Build a Machine.

Reset factory progress?

This resets the introduction and blueprints. Your notebook and settings stay safe.

Clear the notebook?

This permanently removes every saved entry from this browser.