Input → Output

Functions as machines

An interactive lesson with 9 steps, about 8 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A function turns each input into exactly one output. $f(x)$ is the output for input $x$.
• The graph is all the points $(x, f(x))$.
• A curve is a function’s graph only if every vertical line crosses it at most once.

Steps

1. Feed the machine
2. Function notation
3. Evaluate
4. Careful with negatives
5. Find the rule
6. Graphs are pictures of functions
7. Function or not?
8. The vertical line test
9. Run it backwards