The marks scored by five students in a business mathematics test are given below:
| Roll No. (x) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Marks (y) | 45 | 60 | 45 | 78 | 60 |
Write this information as a set of ordered pairs, and examine whether it represents a relation that is a function from the set of roll numbers to the set of marks. Justify your answer, and state the domain and range.
Ordered pairs. Reading the table row by row:
Checking the function conditions. Every roll number through appears exactly once as a first co-ordinate, and each is paired with exactly one mark. It does not matter that the mark is repeated (for roll numbers 1 and 3) or that is repeated (for roll numbers 2 and 5) — the function condition only requires that each input (roll number) has a single output; it places no restriction on outputs repeating. So this relation is a function.
Domain = set of roll numbers actually used = .
Range = set of distinct marks actually obtained = (listed once each, even though and each occur twice).
Independent cross-check: counting the table directly — 5 roll numbers, 5 ordered pairs, no roll number missing and none repeated as a first element — confirms the function condition holds exactly as concluded.
Yes, this is a function. Domain = {1, 2, 3, 4, 5}; Range = {45, 60, 78}.
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