Question

rachel likes to read books. she records the number of books she read over a period of 5 weeks. the set of ordered pairs below gives the details, where the x - coordinate is the number of weeks since she starts recording and the y - coordinate is the number of books she read each week.\\{ (1,2), (2,3), (3,1), (4,4), (5,2) \\}\
which of the following describes the set of ordered pairs?\
\\(\bigcirc\\) a. a relation only\
\\(\bigcirc\\) b. a function only\
\\(\bigcirc\\) c. neither a function nor a relation\
\\(\bigcirc\\) d. both a relation and a function

Explanation:

1. Define Relation and Function: A relation is any set of ordered pairs. A function is a relation where each input (x - value) has exactly one output (y - value).
2. Check if it's a Relation: The given set \(\{(1,2),(2,3),(3,1),(4,4),(5,2)\}\) is a set of ordered pairs, so it is a relation.
3. Check if it's a Function: For each \(x\) - value (1, 2, 3, 4, 5), there is exactly one \(y\) - value. No \(x\) - value is repeated with different \(y\) - values. So it is also a function. Thus, the set is both a relation and a function.

Answer:

D. both a relation and a function