FUN003 · Functions & graphs · Classes 10–12
Vertical line test
The vertical line test: a graph is a function of x if no vertical line meets it more than once. A circle fails; a parabola passes.
| testVertical line test
📐 Formula
graph is a function ⇔ every vertical line x = c meets it at most once
✏️ Worked example
Circle x² + y² = 9: the line x = 1 meets it twice, at y = ±2.83, so it is not a function. Switch to the parabola: always once.
🌍 Where it is used
Checking whether a graph or data set can be modelled by y = f(x).
❓ Quick check
Which graph fails the vertical line test?
🏋️ Practice
EasyDoes y = x³ pass?
Answer: Yes
MediumDoes x = y² pass?
Answer: No
ChallengeDoes a horizontal line y = 3 pass?
Answer: Yes