Today is rung 8 of 8 on this topic
What a function is
Can do: Determines whether a relation is a function and uses function notation confidently.
Why it matters
The concept underpins all later maths. f(x) confusion — reading it as multiplication — is startlingly common and easy to fix.
What it looks like when it's wobbly
Thinks f(x) means f times x, and can't say why the vertical line test works.
⏱️ Two-minute check
"If f(x) = 3x + 1, what's f(4)? Is a circle a function? Why?"
Solid looks like: 13, no, and something about one input giving two outputs.
The full activity for this topic · 20 minutes
The Machine
- 1Draw a machine box: input goes in, output comes out, the rule is inside.
- 2Feed numbers in and record the outputs in a table.
- 3Introduce the notation: f(4) = 13 just names the output for input 4.
- 4Show a broken machine that gives two different outputs for the same input — that's not a function.
- 5Do the vertical line test on graphs and connect it back to the broken machine.
If it's too hard
Input-output tables with no notation.
If it's too easy
Compose functions, and interpret f(x) in a real context like cost as a function of hours.
Say this
"f(4) doesn't mean f times 4. It means: put 4 into the machine, what comes out?"