JayKayElle™All games Function Factory

The Dollhouse family presents

Function Factory

Every machine follows a rule. Can you discover it?

Factory field guide

How functions work

Input

The number that goes into a machine.

4→+ 3→7

Output

The output is the number you get after using the rule.

Rule

The exact instructions a machine uses every time.

Test every row

A rule you guess must work for every example.

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 dot shows an input and its output. The x spot shows the input. The y spot shows the output.

Fractions

A function is a rule. It can give an exact decimal or fraction. Try 0.75 or 3/4.

Nonlinear rules

Squaring means a number times itself. Absolute value means how far from zero. Compare both.

Ambiguity

A few examples may fit many rules. Try more examples. State the pattern as a clear 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

All factory tools are open

Find graphs and fractions on the map. Test rules in Explore or Build a Machine.

Reset factory progress?

This starts the first lesson again and clears blueprints. Your notebook and settings stay safe.

Clear the notebook?

This permanently removes every saved entry from this browser.

Import notebook entries