Function Machine: crack the secret rule.

How to play Function Machine

1. Pick a machine on the map. Tier 1 rules take one step, tier 2 take two (like 2x + 1), and tier 3 use squares, cubes and doubling.
2. Tap a number to feed it in. The output drops out of the chute, joins the table and appears on the graph.
3. When you can see the pattern, press I've cracked it and predict three outputs, including big numbers you didn't try.
4. Then name the rule using x for the input, such as 3x - 2 or x^2 + 1.
5. Use few tries and predict correctly for three stars.

Tips and strategy

• Feed 0 first: whatever comes out is the number added at the end (for two-step rules).
• Feed 1, 2, 3 in order and look at how much the output goes up each time: that is the multiplier.
• If the jumps themselves grow (1, 3, 5, 7…), the rule has a square in it.
• A straight line on the graph means a linear rule like 2x + 1; a curve means powers.