Modelling Real-World Scenarios?
In a school, the number of students attending a library is directly proportional to the number of books it stocks. If the library currently stocks 300 books and has 90 students, can you define a linear function to find the number of students likely to visit the library when it stocks 450 books?
1 Answer
📌 CONCEPT: A relation between two variables is a set of ordered pairs, whereas a function is a relation with each element in the domain having a unique image in the range.
📐 RULE / FORMULA: The rule/formula that defines a function is f(x) = y, where x is the input and y is the output.
💡 WORKED EXAMPLE: Let's say we have a relation {(2, 4), (3, 6), (4, 8)} and we want to check if it's a function. We can see that each element in the domain (2, 3, 4) has a unique image in the range (4, 6, 8). Therefore, this relation is a function.
⚠️ COMMON MISTAKE: Students often confuse relations and functions, thinking they are the same. However, a relation can be a function or not, depending on whether each element in the domain has a unique image in the range.
14 Oct 26
🔗 More from Relations and Functions
Practice this chapter
Get AI-generated board exam questions, track your mastery, and identify weak spots.
Start Free →