Give 5 examples of real life not functions
The Correct Answer and Explanation is:
Five real-life relations that are not mathematical functions
| # | Relation (input → possible outputs) | Why it fails the “one input → one output” rule |
|---|---|---|
| 1 | A person → home addresses | Many people have lived at several addresses, so one person can map to multiple homes. |
| 2 | A single calendar day → air temperature | Temperature changes hour by hour; one day can yield dozens of readings. |
| 3 | A movie → its actors | Every film stars a cast, so one movie corresponds to many actors. |
| 4 | A university student → current courses | Students typically register for several classes each term. |
| 5 | A country → official languages | Multilingual nations (e.g., South Africa) list several official tongues. |
explanation
In mathematics, a function demands that each input from its domain be paired with exactly one output in the codomain. The “vertical line test” for graphs embodies the same requirement: no vertical line may intersect the graph more than once. When a real-world relation violates this uniqueness criterion—because a single input naturally links to multiple sensible outputs—it ceases to be a function, even though the relation itself is perfectly meaningful in everyday life.
Take people and home addresses. Over a lifetime a person often inhabits numerous residences; listing “all addresses ever” immediately assigns multiple outputs to one person. A function could be salvaged only by restricting the rule (e.g., “current address only”), but in its unrestricted form the relation is non-functional.
Daily air temperature illustrates the same point from continuous data. A single date such as 2 June 2025 produces a temperature curve that might range from a chilly dawn to a hot afternoon. Because the day input spawns many temperature outputs, the mapping breaks the uniqueness clause.
Films and their actors highlight non-functionality in categorical data. A feature like Avengers: Endgame links simultaneously to Robert Downey Jr., Scarlett Johansson, and dozens more, so the input “movie” cannot be tied to a lone performer.
Likewise, a student’s course load and a country’s official languages both naturally associate one identifier with several valid attributes—multiple modules on a timetable or several constitutionally recognized tongues—making the plain relation a set-valued map rather than a function.
Recognizing these non-functions is valuable because it reminds us that many authentic relationships are multivalued; mathematics often forces us to restructure or restrict such relations before functional tools (derivatives, compositions, inverses) become applicable.
