TwiddleLab / Math / Functions You Can See
A Function Is a Machine
What you will learn
- A function is a machine: each input gives exactly one output.
- A rule, a table and a graph are three views of the same function.
- Write it as f(x) = 2x + 1: f is the machine, x is what goes in.
How the lesson goes
A mystery machine. A number goes in, a different number comes out.
Feed it. Tap each ball.
Where does 10 come out?
Drag the marker on the output ruler to your guess, then Check. The machine will run it.
Now run it yourself. Light up all five rows.
Slide the input from 0 to 4. The ball, the table row and the dot on the graph move together.
This machine is a function.
A function is a machine where each input gives exactly one output.
The table lists pairs: 0 gives 1, 1 gives 3, 2 gives 5.
The graph draws each pair as a point: input across, output up.
The rule says what happens inside: times 2, then plus 1. We write f(x) = 2x + 1.
Build a machine that turns 3 into 10.
Tap or drag tiles into the slots. Your machine runs 0 to 4 and draws its own table and line.
Game: crack the code.
A new sealed machine. Feed it as many numbers as you like, build its rule from tiles, then Test. Fewest feeds wins.
Your machine meets a taxi meter.
The meter is the Rocket app: $2 to get in, $2 per km. Tap each ride length to run both machines.
Next lesson: Slope Is a Rate · Part of the course: Functions You Can See
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